Answer:
D. 31
Step-by-step explanation:
Given:
[tex] f(x) = 4x^3 - 10 [/tex]
[tex] g(x) = \frac{3x - 4}{2} [/tex]
Required:
The value of g(f(2))
First, find f(2).
Substitute x = 2 into [tex] f(x) = 4x^3 - 10 [/tex].
[tex] f(2) = 4(2)^3 - 10 [/tex]
[tex] f(2) = 4*8 - 10 = 32 - 10 [/tex]
[tex] f(2) = 22 [/tex]
Next, find g(f(2)).
[tex] g(f(x)) = \frac{3(22) - 4}{2} [/tex]
[tex] g(f(x)) = \frac{66 - 4}{2} [/tex]
[tex] g(f(x)) = \frac{62}{2} [/tex]
[tex] g(f(x)) = \frac{62}{2} [/tex]
[tex] g(f(x)) = 31 [/tex]
