Question

let f(x) = 4x - 6 and g(x) = x + 1. find f(g(x)) and g(f(x)).
f(g(x)) = \square (simplify your answer.)

Explanation:

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

To find \( f(g(x)) \), we substitute \( g(x) = x + 1 \) into the function \( f(x) \). So we replace every \( x \) in \( f(x) = 4x - 6 \) with \( g(x) \), which gives us \( f(g(x)) = 4(g(x)) - 6 \).

Step2: Substitute the expression for g(x)

Now we substitute \( g(x)=x + 1 \) into the equation from Step 1. So we have \( f(g(x))=4(x + 1)-6 \).

Step3: Simplify the expression

First, distribute the 4 in \( 4(x + 1) \): \( 4\times x+4\times1 = 4x + 4 \). Then subtract 6: \( 4x+4 - 6=4x - 2 \).

Answer:

\( 4x - 2 \)