Question

let $f(x) = 4x - 6$ and $g(x) = x + 1$. find $f(g(x))$ and $g(f(x))$.
$f(g(x)) = 4x - 2$ (simplify your answer.)
$g(f(x)) = \square$ (simplify your answer.)

Explanation:

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

To find \( g(f(x)) \), we substitute \( f(x) = 4x - 6 \) into \( g(x) \). So we replace \( x \) in \( g(x) = x + 1 \) with \( 4x - 6 \).
\[
g(f(x)) = (4x - 6) + 1
\]

Step2: Simplify the expression

Now we simplify the expression \( (4x - 6) + 1 \). Combine the constant terms: \( -6 + 1 = -5 \).
\[
g(f(x)) = 4x - 5
\]

Answer:

\( 4x - 5 \)