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pretraining/mathematica/algebra/invert_function/1004.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{-8 x-\frac{13}{3}}$
+Answer:
+$\left\{\left\{x\to \frac{1}{24} \left(-3 y^3-13\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1098.txt

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

pretraining/mathematica/algebra/invert_function/1237.txt

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+Problem:
+Find the inverse of the following function: $\sinh \left(5-\frac{x}{2}\right)$
+Answer:
+$\left\{\left\{x\to 10-2 \sinh ^{-1}(y)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1408.txt

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

pretraining/mathematica/algebra/invert_function/1533.txt

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+Problem:
+Find the inverse of the following function: $-\tan ^{-1}\left(8 x+\frac{5}{3}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$-\frac{\tan (y)}{8}-\frac{5}{24}\text{ if }-\frac{\pi }{2}<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1607.txt

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+Problem:
+Find the inverse of the following function: $\tanh (5 x+4)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{5} \tanh ^{-1}(y)-\frac{4}{5}\text{ if }-1<y<1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1634.txt

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

pretraining/mathematica/algebra/invert_function/1707.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{2 x+8}$
+Answer:
+$\left\{\left\{x\to \frac{1}{2} \left(y^3-8\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1762.txt

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+Problem:
+Find the inverse of the following function: $\tanh (8-5 x)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{8}{5}-\frac{1}{5} \tanh ^{-1}(y)\text{ if }-1<y<1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/1844.txt

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

pretraining/mathematica/algebra/invert_function/1883.txt

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

pretraining/mathematica/algebra/invert_function/1948.txt

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+Problem:
+Find the inverse of the following function: $\sqrt[3]{\frac{11 x}{3}+\frac{5}{3}}$
+Answer:
+$\left\{\left\{x\to \frac{1}{11} \left(3 y^3-5\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2166.txt

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

pretraining/mathematica/algebra/invert_function/2210.txt

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+Problem:
+Find the inverse of the following function: $-\sin ^{-1}\left(2-\frac{26 x}{3}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{26} (3 \sin (y)+6)\text{ if }-\frac{\pi }{2}\leq y\leq \frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2281.txt

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

pretraining/mathematica/algebra/invert_function/2298.txt

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+Problem:
+Find the inverse of the following function: $\sqrt{3-6 x}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{6} \left(3-y^2\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2588.txt

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+Problem:
+Find the inverse of the following function: $\frac{2 \cos ^{-1}(4-9 x)}{\pi }$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{9} \left(4-\cos \left(\frac{\pi  y}{2}\right)\right)\text{ if }0\leq y\leq 2$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2612.txt

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

pretraining/mathematica/algebra/invert_function/2615.txt

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+Problem:
+Find the inverse of the following function: $\frac{1}{\frac{11 x}{2}+5}$
+Answer:
+$\left\{\left\{x\to \frac{2-10 y}{11 y}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2724.txt

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+Problem:
+Find the inverse of the following function: $\sinh (4 x+7)$
+Answer:
+$\left\{\left\{x\to \frac{1}{4} \sinh ^{-1}(y)-\frac{7}{4}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2903.txt

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+Problem:
+Find the inverse of the following function: $\sin ^{-1}(5-8 x)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{8} (5-\sin (y))\text{ if }-\frac{\pi }{2}\leq y\leq \frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/2944.txt

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+Problem:
+Find the inverse of the following function: $\tan ^{-1}\left(e^{-3 x-\frac{19}{5}}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$-\frac{1}{3} \log (\tan (y))-\frac{19}{15}\text{ if }0<y<\frac{\pi }{2}$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3054.txt

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+Problem:
+Find the inverse of the following function: $\log \left(\sqrt[3]{x+5}\right)$
+Answer:
+$\left\{\left\{x\to e^{3 y}-5\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3121.txt

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

pretraining/mathematica/algebra/invert_function/3165.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}\left(-2 x-\frac{8}{3}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{6} (-3 \cos (y)-8)\text{ if }0\leq y\leq \pi $}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3169.txt

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+Problem:
+Find the inverse of the following function: $e^{4 x-4} \sqrt{e^{-7 x-1}}$
+Answer:
+$\left\{\left\{x\to \fbox{$2 \log \left(e^{9/2} y\right)\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3195.txt

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

pretraining/mathematica/algebra/invert_function/3395.txt

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+Problem:
+Find the inverse of the following function: $\tanh (4-6 x)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{2}{3}-\frac{1}{6} \tanh ^{-1}(y)\text{ if }-1<y<1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3440.txt

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

pretraining/mathematica/algebra/invert_function/3454.txt

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+Problem:
+Find the inverse of the following function: $\frac{1}{\frac{7 x}{2}+\frac{13}{2}}$
+Answer:
+$\left\{\left\{x\to \frac{2-13 y}{7 y}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/3641.txt

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+Problem:
+Find the inverse of the following function: $e^{\frac{x}{3}+\frac{19}{3}}$
+Answer:
+$\{\{x\to \fbox{$3 \log (y)-19\text{ if }y>0$}\}\}$

pretraining/mathematica/algebra/invert_function/3926.txt

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

pretraining/mathematica/algebra/invert_function/403.txt

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+Problem:
+Find the inverse of the following function: $\cosh (x+7)$
+Answer:
+$\left\{\left\{x\to \fbox{$-\cosh ^{-1}(y)-7\text{ if }y\geq 1$}\right\},\left\{x\to \fbox{$\cosh ^{-1}(y)-7\text{ if }y\geq 1$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4200.txt

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

pretraining/mathematica/algebra/invert_function/4236.txt

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+Problem:
+Find the inverse of the following function: $e^{4 x+5}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{\log (y)}{4}-\frac{5}{4}\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4384.txt

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+Problem:
+Find the inverse of the following function: $\log (5)-\tanh \left(5 x+\frac{14}{3}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$-\frac{1}{5} \tanh ^{-1}(y-\log (5))-\frac{14}{15}\text{ if }-1+\log (5)<y<1+\log (5)$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4437.txt

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+Problem:
+Find the inverse of the following function: $\sinh \left(\frac{5 x}{2}+\frac{13}{2}\right)$
+Answer:
+$\left\{\left\{x\to \frac{2}{5} \sinh ^{-1}(y)-\frac{13}{5}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4535.txt

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+Problem:
+Find the inverse of the following function: $-e^{-6 x-7} \sin (3)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{6} \log \left(-\frac{\sin (3)}{y}\right)-\frac{7}{6}\text{ if }y<0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4603.txt

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+Problem:
+Find the inverse of the following function: $\log \left(-7 x-\frac{13}{3}\right)$
+Answer:
+$\left\{\left\{x\to \frac{1}{21} \left(-3 e^y-13\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4873.txt

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+Problem:
+Find the inverse of the following function: $\log \left(\sqrt[3]{5 x-8}\right)$
+Answer:
+$\left\{\left\{x\to \frac{1}{5} \left(e^{3 y}+8\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/4970.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}\left(3 x+\frac{13}{5}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{15} (5 \cos (y)-13)\text{ if }0\leq y\leq \pi $}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5115.txt

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+Problem:
+Find the inverse of the following function: $2 \sqrt{2} \sqrt{x}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{y^2}{8}\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5181.txt

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+Problem:
+Find the inverse of the following function: $\cos ^{-1}\left(-3 x-\frac{5}{2}\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{6} (-2 \cos (y)-5)\text{ if }0\leq y\leq \pi $}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5228.txt

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

pretraining/mathematica/algebra/invert_function/5434.txt

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+Problem:
+Find the inverse of the following function: $\sinh \left(\cos ^{-1}(6 x+6)\right)$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{1}{6} \left(\cos \left(\sinh ^{-1}(y)\right)-6\right)\text{ if }0\leq y\leq \sinh (\pi )$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5605.txt

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

pretraining/mathematica/algebra/invert_function/5629.txt

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+Problem:
+Find the inverse of the following function: $\log (8 x+5)$
+Answer:
+$\left\{\left\{x\to \frac{1}{8} \left(e^y-5\right)\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5789.txt

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+Problem:
+Find the inverse of the following function: $-\sin (\tanh (3 x+4))$
+Answer:
+$\left\{\left\{x\to \fbox{$-\frac{1}{3} \tanh ^{-1}\left(\sin ^{-1}(y)\right)-\frac{4}{3}\text{ if }-\sin (1)<y<\sin (1)$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5885.txt

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+Problem:
+Find the inverse of the following function: $e^{4 x+\frac{5}{2}}$
+Answer:
+$\left\{\left\{x\to \fbox{$\frac{\log (y)}{4}-\frac{5}{8}\text{ if }y>0$}\right\}\right\}$

pretraining/mathematica/algebra/invert_function/5947.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}$}\right\}\right\}$