Question

question 11 of 45
given functions ( f(x) = 4x + 3 ) and ( g(x) = x^2 - 2 ), what is the value of ( f(g(-3)) )?
a (-83)
b (-41)
c (31)
d (79)

Explanation:

Step1: Calculate \( g(-3) \)

First, we need to find the value of \( g(-3) \) using the function \( g(x)=x^{2}-2 \). Substitute \( x = -3 \) into \( g(x) \):
\( g(-3)=(-3)^{2}-2 \)
\( = 9 - 2 \)
\( = 7 \)

Step2: Calculate \( f(g(-3)) \)

Now that we know \( g(-3)=7 \), we substitute this value into the function \( f(x)=4x + 3 \) to find \( f(g(-3))=f(7) \). Substitute \( x = 7 \) into \( f(x) \):
\( f(7)=4\times7 + 3 \)
\( = 28 + 3 \)
\( = 31 \)

Answer:

C. 31