Answered

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

Consider Functions Fand G Fx 13 Gx 18x1 class=

Sagot :

Absor201idn

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.            

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