Answer:
We conclude that
(g o f) (4) = 9
Hence, option C is correct.
Step-by-step explanation:
Given
f(x) = -x³
g(x) = |1/8x - 1|
To determine
(g o f) (4) = ?
Using the formula
(g o f) (4) = g[(f(4)]
first we need to determine f(4)
so substituting x = 4 into f(x) = -x³
f(x) = -x³
f(4) = -(4)³ = -64
so
(g o f) (4) = g[(f(4)] = g(-64)
so substitute x = -64 in g(x) = |1/8x - 1|
[tex]g\left(x\right)=\left|\frac{1}{8}x-1\right|[/tex]
substitute x = -64
[tex]g\left(-64\right)=\left|\frac{1}{8}\left(-64\right)-1\right|[/tex]
[tex]=\left|-\frac{1}{8}\cdot \:64-1\right|[/tex]
[tex]=\left|-8-1\right|[/tex]
[tex]=\left|-9\right|[/tex]
Apply absolute rule: |-a| = a
[tex]=9[/tex]
Therefore, we conclude that
(g o f) (4) = 9
Hence, option C is correct.
