Question

In Problems 9–23, 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.

$\cos \left({\cos }^{-1}0.6\right)$

Short answer

The exact value of the composite function is$0.6.$

Step-by-step solution

Step 1. Given Information

The given composite function is $\cos \left({\cos }^{-1}0.6\right).$

We have to find the exact value.

Step 2. Finding the value

By using the properties of an inverse function, $f\left(f^{-1}\left(x\right)\right)=\cos \left({\cos }^{-1}x\right)=xwhere-1\le x\le 1$

So,$\cos \left({\cos }^{-1}0.6\right)=0.6$