Chapter 1.2, Problem 61E

To determine

To find: The correct option for the value of function $\left(f\circ g\right)\left(2\right)$ .

Answer to Problem 61E

The correct option is (D) and the value of the function $\left(f\circ g\right)\left(2\right)$ is $9$ .

Explanation of Solution

Given information: The functions are $f\left(x\right)=2x-1$ and $g\left(x\right)=x+3$ .

Substitute $x+3$ for $g\left(x\right)$ in the function $f\left(g\left(x\right)\right)$ .

  $f\left(g\left(x\right)\right)=f\left(x+3\right)$

It is given that $f\left(x\right)=2x-1$ , substitute $x+3$ for $x$ in the function.

  $\begin{array}{c}f\left(x+3\right)=2\left(x+3\right)-1\\ =2x+6-1\\ =2x+5\end{array}$

So, the function $f\left(g\left(x\right)\right)$ is equal to $2x+5$ .

Substitute $2$ for $x$ in the function $f\left(g\left(x\right)\right)$ .

  $\begin{array}{l}f\left(g\left(x\right)\right)=2x+5\\ f\left(g\left(2\right)\right)=2\times 2+5\\ f\left(g\left(2\right)\right)=4+5\\ f\left(g\left(2\right)\right)=9\end{array}$

Therefore, the correct option is (D) and the value of the function $\left(f\circ g\right)\left(2\right)$ is $9$ .