Question

question
given the definitions of f(x) and g(x) below, find the value of f(g(-2)).
f(x) = 3x² - 7x + 15
g(x) = x + 7
answer
attempt 1 out of 2

Explanation:

Step1: Calculate \( g(-2) \)

Given \( g(x) = x + 7 \), substitute \( x = -2 \) into \( g(x) \):
\( g(-2) = -2 + 7 = 5 \)

Step2: Calculate \( f(g(-2)) = f(5) \)

Given \( f(x) = 3x^2 - 7x + 15 \), substitute \( x = 5 \) into \( f(x) \):
\( f(5) = 3(5)^2 - 7(5) + 15 \)
First, calculate \( (5)^2 = 25 \), then \( 3\times25 = 75 \), \( 7\times5 = 35 \)
So, \( f(5) = 75 - 35 + 15 = 55 \)

Answer:

55