Question

let f(x) = 5x - 6 and g(x) = x + 3. find f(g(x)) and g(f(x)).
f(g(x)) = \boxed{} (simplify your answer.)

Explanation:

Step1: Substitute g(x) into f(x)

Since \( g(x)=x + 3 \), we substitute \( x+3 \) for \( x \) in \( f(x)=5x - 6 \). So we get \( f(g(x))=f(x + 3)=5(x + 3)-6 \).

Step2: Distribute and simplify

First, distribute the 5 in \( 5(x + 3) \): \( 5(x + 3)=5x+15 \). Then subtract 6: \( 5x + 15-6=5x+9 \).

Answer:

\( 5x + 9 \)