Chapter 3.1, Problem 6QR

To determine

To write : $\sqrt{\cos x+2}$ as a composite of two or more of $f,g$ and, $h$ .

Answer to Problem 6QR

The composite function of $\sqrt{\cos x+2}$ is $g\left(f\left(x\right)\right)$ .

Explanation of Solution

Given information :

  $f\left(x\right)=\cos x,g\left(x\right)=\sqrt{x+2}$ , and $h\left(x\right)=3x^2$ .

Since, $g\left(x\right)=\sqrt{x+2}$ .

Replace $x$ by $\cos x$ in the function $g\left(x\right)=\sqrt{x+2}$ .

  $g\left(\cos x\right)=\sqrt{\cos x+2}$

But $f\left(x\right)=\cos x$ , replace $\cos x$ by $f\left(x\right)$ on left side of the above function.

  $g\left(f\left(x\right)\right)=\sqrt{\cos x+2}$