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

Explanation:

Step1: Calculate f(2)

To find ( f(2) ), substitute ( x = 2 ) into the function ( f(x)=4x^{3}-10 ). [ \begin{align*} f(2)&=4\times(2)^{3}-10\ &=4\times8 - 10\ &=32 - 10\ &= 22 \end{align*} ]

Step2: Calculate g(f(2))

Now that we know ( f(2) = 22 ), we substitute ( x = 22 ) into the function ( g(x)=\frac{3x - 4}{2} ). [ \begin{align*} g(22)&=\frac{3\times22-4}{2}\ &=\frac{66 - 4}{2}\ &=\frac{62}{2}\ &= 31 \end{align*} ] Wait, this is a mistake. Wait, let's recalculate ( f(2) ) again. Wait, ( 4\times2^{3}=4\times8 = 32 ), ( 32-10 = 22 ). Then ( g(22)=\frac{3\times22 - 4}{2}=\frac{66 - 4}{2}=\frac{62}{2}=31 )? But let's check the options. Option D is 31. But wait, maybe I made a mistake. Wait, no, let's check again.

Wait, ( f(x)=4x^{3}-10 ), so ( f(2)=4*(8)-10=32 - 10 = 22 ). Then ( g(x)=\frac{3x - 4}{2} ), so ( g(22)=\frac{3*22 - 4}{2}=\frac{66 - 4}{2}=\frac{62}{2}=31 ). So the answer should be D.

Wait, but let me check again. Wait, maybe I misread the function. Wait, the function ( g(x)=\frac{3x - 4}{2} ). So when ( x = 22 ), ( 3*22 = 66 ), ( 66 - 4 = 62 ), ( 62/2 = 31 ). So yes, that's correct.

Answer:

D. 31