Question

select the correct answer.
consider these functions:
$f(x) = 4x^3 - 10$
$g(x) = \frac{3x - 4}{2}$
what is the value of $g(f(2))$?
a. -6
b. 2
c. 19
d. 31

Explanation:

Step1: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) = 4x^3 - 10 \).
\( f(2) = 4\times(2)^3 - 10 = 4\times8 - 10 = 32 - 10 = 22 \)

Step2: Calculate \( g(f(2)) \)

Substitute \( f(2) = 22 \) into \( g(x) = \frac{3x - 4}{2} \).
\( g(22) = \frac{3\times22 - 4}{2} = \frac{66 - 4}{2} = \frac{62}{2} = 31 \)

Answer:

D. 31