Chapter 1.5, Problem 38E

To determine

To find: $\left[g\circ h\right]\left(x\right)$

Answer to Problem 38E

  $x^2-1$

Explanation of Solution

Given information:

  $\begin{array}{l}g\left(x\right)=x-1\\ h\left(x\right)=x^2\end{array}$

Calculation:

The composition for the function can be solved as follows:

  $\begin{array}{c}\left[g\circ h\right]\left(x\right)=g\left(h\left(x\right)\right)\\ =h\left(x\right)-1\left[\text{Put }h\left(x\right)\text{ into }f\left(x\right)\right]\\ =x^2-1\left[\text{Put value of }h\left(x\right)\right]\end{array}$

The value $\left[g\circ h\right]\left(x\right)$ is $x^2-1$ .