Question

Consider functions fand g.¡(I) =-23g(I)- 1What is the value of (g o /) (4),OA.}O B.9OC.O D.-9

Answer 1

Answer:

B. 9

Explanation:

Given f(x) and g(x) below:

$\begin{aligned}&f(x)=-x^{3} \\&g(x)=\left|\frac{1}{8} x-1\right|\end{aligned}$

We want to find the value of the composition (g o f)(4).

$(g\circ f)(4)=g[f(4)]$

First, find the value of f(4).

$\begin{gathered} \begin{equation*} f(x)=-x^3 \end{equation*} \\ \implies f(4)=-4^3=-64 \end{gathered}$

Next, substitute f(4) into g[f(4)].

$\begin{gathered} g[f(4)]=g(-64) \\ \begin{equation*} g(x)=\left|\frac{1}{8}x-1\right| \end{equation*} \\ \implies g(-64)=\left|\frac{1}{8}(-64)-1\right|=|-8-1|=|-9| \\ \text{The absolute symbol always gives a positive result.} \\ \begin{equation*} |-9|=9 \end{equation*} \\ \implies(g\circ f)(4)=9 \end{gathered}$

The value of (g o f)(4) is 9.

The correct choice is B.