Chapter 1.8, Problem 32E

a.

To determine

To find:The value of $f\circ g$ .

Answer to Problem 32E

The value of $f\circ g$ is $3x^4$ .

Explanation of Solution

Given information:

The given functions are $f\left(x\right)=3x$ and $g\left(x\right)=x^4$ .

Calculation:

The value of composition of $f$ with $g$ .

  $\begin{array}{c}f\circ g\left(x\right)=f\left(g\left(x\right)\right)\\ =3\left(g\left(x\right)\right)\\ =3x^4\end{array}$

Therefore, the value of $f\circ g$ is $3x^4$ .

b.

To determine

To find: The value of $g\circ f$ .

Answer to Problem 32E

The value of $g\circ f$ is $81x^4$ .

Explanation of Solution

Given information:

The given functions are $f\left(x\right)=3x$ and $g\left(x\right)=x^4$ .

Calculation:

The value of composition of $g$ with $f$ .

  $\begin{array}{c}g\circ f\left(x\right)=g\left(f\left(x\right)\right)\\ ={\left(f\left(x\right)\right)}^4\\ ={\left(3x\right)}^4\\ =81x^4\end{array}$

Therefore, the value of $g\circ f$ is $81x^4$ .

c.

To determine

To find: The value of $g\circ g$ .

Answer to Problem 32E

The value of $g\circ g$ is $x^{16}$ .

Explanation of Solution

Given information:

The given functions are $f\left(x\right)=3x$ and $g\left(x\right)=x^4$ .

Calculation:

The value of composition of $g$ with $g$ .

  $\begin{array}{c}g\circ g\left(x\right)=g\left(g\left(x\right)\right)\\ ={\left(g\left(x\right)\right)}^4\\ ={\left(x^4\right)}^4\\ =x^{16}\end{array}$

Therefore, the value of $g\circ g$ is $x^{16}$ .