Chapter 6.4, Problem 81AYU

To determine

To calculate: $(f\circ g)(x)$ and $(g\circ f)(x)$ and graph of each function.

Answer to Problem 81AYU

Solution: $\begin{array}{l}(f\circ g)(x)=\sin 4x\\ (g\circ f)(x)=4\sin (x)\end{array}$

Explanation of Solution

  $\begin{array}{l}f(x)=\sin x\\ g(x)=4x\\ f\circ g(x)=\sin (g(x))=\sin 4x\\ g\circ f(x)=4(f(x))=4\sin (x)\end{array}$

Plots of $(f\circ g)(x)$ and $(g\circ f)(x)$ are given as