Question

let f(x) = 5x - 6 and g(x) = x + 3. find f(g(x)) and g(f(x)).
f(g(x)) = 5x + 9 (simplify your answer.)
g(f(x)) = \square (simplify your answer.)

Explanation:

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

We know that \( g(x)=x + 3 \) and \( f(x)=5x-6 \). To find \( g(f(x)) \), we substitute \( f(x) \) in place of \( x \) in the function \( g(x) \). So we get \( g(f(x))=f(x)+3 \).

Step2: Replace f(x) with its expression

Since \( f(x) = 5x-6 \), we substitute this into the equation from Step 1. So \( g(f(x))=(5x - 6)+3 \).

Step3: Simplify the expression

Simplify \( (5x-6)+3 \) by combining like terms. \( -6 + 3=-3 \), so the expression simplifies to \( 5x-3 \).

Answer:

\( 5x - 3 \)