Question

Consider functions fand g. f(x) = -13 g(x) = |1/8x-1|

Answer 1

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|

$g\left(x\right)=\left|\frac{1}{8}x-1\right|$

substitute x = -64

$g\left(-64\right)=\left|\frac{1}{8}\left(-64\right)-1\right|$

            $=\left|-\frac{1}{8}\cdot \:64-1\right|$

            $=\left|-8-1\right|$

            $=\left|-9\right|$

Apply absolute rule: |-a| = a

            $=9$

Therefore, we conclude that

(g o f) (4) = 9

Hence, option C is correct.