Chapter 1.3, Problem 2QQ

To determine

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

Answer to Problem 2QQ

The correct option is (D) as the value of $f\circ g\left(2\right)$ is $10$ .

Explanation of Solution

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

Calculation:

The value of $f\circ g\left(2\right)$ is equal to $f\left(g\left(2\right)\right)$ .

Substitute 2 for $x$ in the function $g\left(x\right)=2x-1$ to calculate $g\left(2\right)$ .

  $\begin{array}{c}g\left(2\right)=2\times 2-1\\ g\left(2\right)=4-1\\ g\left(2\right)=3\end{array}$

So, $f\left(g\left(2\right)\right)=f\left(3\right)$ . Now, calculate the value $f\left(3\right)$ .

  $\begin{array}{c}f\left(x\right)=x^2+1\\ f\left(3\right)=3^2+1\\ f\left(3\right)=9+1\\ f\left(3\right)=10\end{array}$

Therefore, the correct option is (D) as the value of $f\circ g\left(2\right)$ is $10$ .