Question

$\tan ({\tan }^{-1}x)=xwhere\_\_\_\_\_.$

Short answer

$\tan ({\tan }^{-1}x)=xwhere\mathbf{-}\mathbf{\infty }\mathbf{<}\mathit{x}\mathbf{<}\mathbf{\infty }.$

Step-by-step solution

Step 1. Given Information:

Given expression:

$\tan ({\tan }^{-1}x)=xwhere\_\_\_\_\_.$

We want to fill the gap in given expression.

Step 2. Solution:

The tangent function and its inverse has the property:

$f\left(f^{-1}\right(x\left)\right)=\tan ({\tan }^{-1}x)=xwhere-\infty <x<\infty .$

Therefore,$\tan ({\tan }^{-1}x)=xwhere-\infty <x<\infty .$