Chapter 3.1, Problem 1QR

To determine

To write : a simplified expression for the composite function $f\left(g\left(x\right)\right)$ .

Answer to Problem 1QR

The composite function $f\left(g\left(x\right)\right)$ is $\sin \left(x^2+1\right)$ .

Explanation of Solution

Given information :

  $f\left(x\right)=\sin x,g\left(x\right)=x^2+1$ , and $h\left(x\right)=7x$ .

Since, $f\left(x\right)=\sin x$ .

Replace $x$ by $g\left(x\right)$ in above function.

  $f\left(g\left(x\right)\right)=\sin g\left(x\right)$

Substitute $g\left(x\right)=x^2+1$ in the right side of above function.

  $f\left(g\left(x\right)\right)=\sin \left(x^2+1\right)$

Hence, the composite function $f\left(g\left(x\right)\right)$ is $\sin \left(x^2+1\right)$ .