select the correct answer. consider these functions: $f(x)=4x^{3}-10$ $g(x)=\frac{3x - 4}{2}$ what is the…

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

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

Answer

Explanation:

Step1: Calculate f(2)

Substitute (x = 2) into (f(x)): [ \begin{align*} f(2)&=4\times2^{3}-10\ &=4\times8 - 10\ &=32-10\ &= 22 \end{align*} ]

Step2: Calculate g(f(2))

Since (f(2)=22), substitute (x = 22) into (g(x)): [ \begin{align*} g(f(2))&=g(22)\ &=\frac{3\times22 - 4}{2}\ &=\frac{66-4}{2}\ &=\frac{62}{2}\ &=31 \end{align*} ]

Answer:

D. 31