Question

by the end of this lesson, you will be able to answer the following questions. given the functions $f(x) = 3x + 2$ and $g(x) = x^2 - 5$, determine the values of each of the following compositions of the functions: 1. $f(g(2))$ 2. $g(f(-3))$ 3. $g(g(3))$ 4. $f(f(x))$ 5. $g(f(x))$

Explanation:

Step1: Find \( g(2) \)

First, we calculate \( g(2) \) using the function \( g(x) = x^2 - 5 \). Substitute \( x = 2 \) into \( g(x) \):
\( g(2) = (2)^2 - 5 = 4 - 5 = -1 \)

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

Now, substitute \( g(2) = -1 \) into the function \( f(x) = 3x + 2 \):
\( f(g(2)) = f(-1) = 3(-1) + 2 = -3 + 2 = -1 \)

Answer:

\( -1 \)