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pretraining/mathematica/algebra/invert_function/1183.txt

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+Problem:
+Find the inverse of the following function: $-\tan ^{-1}(4-2 x)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{\tan (y)}{2}+2\text{ if }-\frac{\pi }{2}<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1270.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{e^{1-6 x}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{3} \log \left(\frac{\sqrt{e}}{y}\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1336.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{\cos ^{-1}\left(\frac{15 x}{2}+1\right)}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{2}{15} \left(\cos \left(y^3\right)-1\right)\text{ if }0\leq y\leq \sqrt[3]{\pi }$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/136.txt

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+Problem:
+Find the inverse of the following function: $e^{2 x-\frac{3}{2}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{2} \log \left(e^{3/2} y\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1495.txt

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+Problem:
+Find the inverse of the following function: $\sinh \left(\frac{15}{2}-3 x\right)$
+Answer:
+$\left\{\left\{x\to \frac{5}{2}-\frac{1}{3} \sinh ^{-1}(y)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1648.txt

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+Problem:
+Find the inverse of the following function: $e^{9 x+5}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{\log (y)}{9}-\frac{5}{9}\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1884.txt

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+Problem:
+Find the inverse of the following function: $-((6 x-1) \csc (4))$
+Answer:
+$\left\{\left\{x\to \frac{1}{6}-\frac{1}{6} y \sin (4)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2049.txt

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+Problem:
+Find the inverse of the following function: $\sin \left(\frac{x}{2}+\frac{9}{2}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$2 \left(-\sin ^{-1}(y)+2 \pi  c_1+\pi \right)-9\text{ if }c_1\in \mathbb{Z}\land -1\leq y\leq 1$}\right\},\left\{x\to \fbox{$2 \left(\sin ^{-1}(y)+2 \pi  c_1\right)-9\text{ if }c_1\in \mathbb{Z}\land -1\leq y\leq 1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2211.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}\left(\frac{7 x}{2}-\frac{11}{2}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{7} (2 \cos (y)+11)\text{ if }0\leq y\leq \pi $}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2377.txt

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+Problem:
+Find the inverse of the following function: $-\sinh (6-5 x)$
+Answer:
+$\left\{\left\{x\to \frac{1}{5} \sinh ^{-1}(y)+\frac{6}{5}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2537.txt

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+Problem:
+Find the inverse of the following function: $e^{-9 x-\frac{11}{2}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{9} \log \left(\frac{1}{y}\right)-\frac{11}{18}\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2638.txt

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+Problem:
+Find the inverse of the following function: $-\tan ^{-1}(6-6 x)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{\tan (y)}{6}+1\text{ if }-\frac{\pi }{2}<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2849.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}\left(\frac{27 x}{5}-\frac{2}{5}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{27} (5 \cos (y)+2)\text{ if }0\leq y\leq \pi $}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2966.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{7 x-\frac{23}{3}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{21} \left(3 y^2+23\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2987.txt

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+Problem:
+Find the inverse of the following function: $\tan ^{-1}(2 x+2)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{\tan (y)}{2}-1\text{ if }-\frac{\pi }{2}<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/308.txt

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+Problem:
+Find the inverse of the following function: $-\tanh \left(3 x+\frac{17}{3}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$-\frac{1}{3} \tanh ^{-1}(y)-\frac{17}{9}\text{ if }-1<y<1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3148.txt

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+Problem:
+Find the inverse of the following function: $\tan ^{-1}\left(\frac{13 x}{2}+5\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{2 \tan (y)}{13}-\frac{10}{13}\text{ if }-\frac{\pi }{2}<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3236.txt

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+Problem:
+Find the inverse of the following function: $\sin ^{-1}\left(\frac{14 x}{5}+\frac{9}{5}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{14} (5 \sin (y)-9)\text{ if }-\frac{\pi }{2}\leq y\leq \frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3344.txt

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+Problem:
+Find the inverse of the following function: $e^{-3 x-8}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{3} \log \left(\frac{1}{y}\right)-\frac{8}{3}\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3376.txt

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+Problem:
+Find the inverse of the following function: $\sinh \left(\sqrt[3]{5-\frac{9 x}{2}}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{9} \left(10-2 \sinh ^{-1}(y)^3\right)\text{ if }y>0\lor y<0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3378.txt

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+Problem:
+Find the inverse of the following function: $\sin ^{-1}(2 x+3)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{2} (\sin (y)-3)\text{ if }-\frac{\pi }{2}\leq y\leq \frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3530.txt

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+Problem:
+Find the inverse of the following function: $-\tanh \left(\frac{2 x}{5}+\frac{21}{5}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$-\frac{5}{2} \tanh ^{-1}(y)-\frac{21}{2}\text{ if }-1<y<1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3553.txt

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+Problem:
+Find the inverse of the following function: $\log \left(x^2+1\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$-\sqrt{-1+e^y}\text{ if }y\geq 0$}\right\},\left\{x\to \fbox{$\sqrt{-1+e^y}\text{ if }y\geq 0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/385.txt

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+Problem:
+Find the inverse of the following function: $\log \left(\sqrt{2-3 x}\right)$
+Answer:
+$\left\{\left\{x\to \frac{1}{3} \left(2-e^{2 y}\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3989.txt

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+Problem:
+Find the inverse of the following function: $\log \left(-6 x-\frac{23}{3}\right)$
+Answer:
+$\left\{\left\{x\to \frac{1}{18} \left(-3 e^y-23\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4030.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{-7 x-7}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{7} \left(-y^2-7\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4039.txt

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+Problem:
+Find the inverse of the following function: $e^{\frac{11 x}{2}+\frac{7}{2}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{2 \log (y)}{11}-\frac{7}{11}\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4131.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}(-3 x-2)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{3} (-\cos (y)-2)\text{ if }0\leq y\leq \pi $}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4354.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{\frac{20 x}{3}+\frac{13}{3}}$
+Answer:
+$\left\{\left\{x\to \frac{1}{20} \left(3 y^3-13\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/441.txt

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+Problem:
+Find the inverse of the following function: $\log \left(\frac{x}{3}-3\right)$
+Answer:
+$\left\{\left\{x\to 3 e^y+9\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4480.txt

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+Problem:
+Find the inverse of the following function: $\sin ^{-1}(6 x+7)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{6} (\sin (y)-7)\text{ if }-\frac{\pi }{2}\leq y\leq \frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4633.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{6-\frac{33 x}{5}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{33} \left(30-5 y^2\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4737.txt

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+Problem:
+Find the inverse of the following function: $\sinh (8 x+4)$
+Answer:
+$\left\{\left\{x\to \frac{1}{8} \sinh ^{-1}(y)-\frac{1}{2}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4871.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}(-4 x-8)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{4} (-\cos (y)-8)\text{ if }0\leq y\leq \pi $}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5236.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{6 x+9}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{6} \left(y^2-9\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5484.txt

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+Problem:
+Find the inverse of the following function: $-\tanh (3-9 x)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{9} \tanh ^{-1}(y)+\frac{1}{3}\text{ if }-1<y<1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5588.txt

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+Problem:
+Find the inverse of the following function: $\log (7-2 x)$
+Answer:
+$\left\{\left\{x\to \frac{1}{2} \left(7-e^y\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5669.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}(x-5)$
+Answer:
+$\{\{x\to \fbox{$\cos (y)+5\text{ if }0\leq y\leq \pi $}\}\}$

pretraining/mathematica/algebra/invert_function/5676.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{3} \sqrt[3]{x}$
+Answer:
+$\left\{\left\{x\to \frac{y^3}{3}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5853.txt

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+Problem:
+Find the inverse of the following function: $\cosh (1-x)$
+Answer:
+$\left\{\left\{x\to \fbox{$1-\cosh ^{-1}(y)\text{ if }y\geq 1$}\right\},\left\{x\to \fbox{$\cosh ^{-1}(y)+1\text{ if }y\geq 1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5864.txt

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+Problem:
+Find the inverse of the following function: $\log \left(-\frac{2 x}{3}-\frac{16}{3}\right)$
+Answer:
+$\left\{\left\{x\to \frac{1}{2} \left(-3 e^y-16\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6042.txt

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+Problem:
+Find the inverse of the following function: $\tan ^{-1}(2-5 x)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{2}{5}-\frac{\tan (y)}{5}\text{ if }-\frac{\pi }{2}<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6176.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{\cos ^{-1}(-7 x-2)}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{7} \left(-\cos \left(y^3\right)-2\right)\text{ if }0\leq y\leq \sqrt[3]{\pi }$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6208.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{4 x+4}$
+Answer:
+$\left\{\left\{x\to \frac{1}{4} \left(y^3-4\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6236.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{\tanh (3 x+8)}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{3} \tanh ^{-1}\left(y^2\right)-\frac{8}{3}\text{ if }0\leq y<1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6423.txt

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+Problem:
+Find the inverse of the following function: $-\sinh \left(4 x+\frac{13}{2}\right)$
+Answer:
+$\left\{\left\{x\to -\frac{1}{4} \sinh ^{-1}(y)-\frac{13}{8}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6619.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{\frac{37 x}{5}-\frac{3}{5}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{37} \left(5 y^2+3\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6629.txt

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+Problem:
+Find the inverse of the following function: $\tan ^{-1}\left(e^{\frac{10 x}{3}+\frac{7}{3}}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{3}{10} \log (\tan (y))-\frac{7}{10}\text{ if }0<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/6941.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{\frac{13}{3}-\frac{x}{3}}$
+Answer:
+$\left\{\left\{x\to 13-3 y^3\right\}\right\}$

pretraining/mathematica/algebra/invert_function/7016.txt

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+Problem:
+Find the inverse of the following function: $\log \left(-\sinh \left(\frac{11 x}{2}+8\right)\right)$
+Answer:
+$\left\{\left\{x\to -\frac{2}{11} \sinh ^{-1}\left(e^y\right)-\frac{16}{11}\right\}\right\}$