Chapter 14.6, Problem 1WE

a.

To determine

To find the value of $\left(gof\right)\left(2\right).$

Answer to Problem 1WE

The value of $\left(gof\right)\left(2\right)\text{ is }1.$

Explanation of Solution

Given two functions: $f\left(x\right)=x^2\text{ and }g\left(x\right)=2x-7.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(2\right)=g\left(f\left(2\right)\right)\\ =g\left(2^2\right)\\ =g\left(4\right)\\ g\left(4\right)=2\cdot 4-7\\ =8-7\\ =1\end{array}$

Thus, the value of $\left(gof\right)\left(2\right)\text{ is }1.$

b.

To determine

To find the value of $\left(gof\right)\left(x\right).$

Answer to Problem 1WE

The value of $\left(gof\right)\left(x\right)\text{ is }2x^2-7.$

Explanation of Solution

Given two functions: $f\left(x\right)=x^2\text{ and }g\left(x\right)=2x-7.$

Calculation:

  $\begin{array}{l}\left(gof\right)\left(x\right)=g\left(f\left(x\right)\right)\\ =g\left(x^2\right)\\ =2x^2-7\end{array}$

Thus, the value of $\left(gof\right)\left(x\right)\text{ is }2x^2-7.$

c.

To determine

To find the value of $fog\left(2\right).$

Answer to Problem 1WE

The value of $\left(fog\right)\left(2\right)\text{ is }9.$

Explanation of Solution

Given two functions: $f\left(x\right)=x^2\text{ and }g\left(x\right)=2x-7.$

Calculation:

  $\begin{array}{l}\left(fog\right)\left(2\right)=f\left(g\left(2\right)\right)\\ =f\left(2\cdot 2-7\right)\\ =f\left(-3\right)\\ ={\left(-3\right)}^2\\ =9\end{array}$

Thus, the value of $\left(fog\right)\left(2\right)\text{ is }9.$

d.

To determine

To find the value of $\left(fog\right)\left(x\right).$

Answer to Problem 1WE

The value of $fog\left(x\right)\text{ is }4x^2-28x+49.$

Explanation of Solution

Given two functions: $f\left(x\right)=x^2\text{ and }g\left(x\right)=2x-7.$

Calculation:

  $\begin{array}{l}fog\left(x\right)=f\left(g\left(x\right)\right)\\ =f\left(2x-7\right)\\ ={\left(2x-7\right)}^2\\ =4x^2-28x+49\end{array}$

Thus, the value of $fog\left(x\right)\text{ is }4x^2-28x+49.$