Question

Find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.

$\tan \left({\tan }^{-1}\left(-2\right)\right)$

Short answer

The value for the given expression

$\tan \left({\tan }^{-1}\left(-2\right)\right)=-2$

Step-by-step solution

Step 1. Given Information

Given trigonometric expression

$\tan \left({\tan }^{-1}\left(-2\right)\right)$

Step 2. Calculation

The value for the given expression

$$\begin{gathered} \tan \left({\tan }^{-1}x\right)=xif-\infty <x<\infty \\ therefore \\ \tan \left({\tan }^{-1}-2\right)=-2 \end{gathered}$$