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

B. 9

Explanation:

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

`\begin{aligned}&f(x)=-x^(3) \\&g(x)=\left|(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|(1)/(8)x-1\right| \end{equation*} \\ \implies g(-64)=\left|(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.