The solution:
Given the functions:
[tex]\begin{gathered} f(x)-x^3 \\ \\ g(x)=|\frac{1}{8}x-1| \end{gathered}[/tex]
Required:
To find the value of g(f(4))
Step 1:
Substitute 4 for x in f(x).
[tex]f(4)=-(4)^3=-64[/tex]
Step 2:
Substitute -64 for x in g(x).
[tex]\begin{gathered} g(-64)=|\frac{1}{8}(-64)-1| \\ \\ g(-64)=|(1\times-8)-1| \\ \\ g(-64)=|-8-1|=|-9|=9 \end{gathered}[/tex]
Therefore, the correct answer is 9 [option C]
