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.

$\cos \left({\cos }^{-1}\left(1.2\right)\right)$.

Short answer

The composite function$\cos \left({\cos }^{-1}\left(1.2\right)\right)$is not defined.

Step-by-step solution

Step 1. Given Information.

The composite function is,$\cos \left({\cos }^{-1}\left(1.2\right)\right)$.

Step 2. Finding the value.

The property of inverse cosine function is,

$f\left(f^{-1}\right(x\left)\right)=\cos \left({\cos }^{-1}\left(x\right)\right)$

$=x$ where $-1\le x\le 1$.

The value $1.2$does not lie in the interval $[-1,1]$which is the domain of the inverse cosine function.

The composite function $\cos \left({\cos }^{-1}\left(1.2\right)\right)$is not defined.