Question

using f(x)=x+1 and g(x)=3x-2, find g(f(x))
3x+1
369
257
4x²-16x+16

Explanation:

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

To find \( g(f(x)) \), we substitute \( f(x) = x + 1 \) into \( g(x) \). So we replace every \( x \) in \( g(x) = 3x - 2 \) with \( f(x) \), which gives us \( g(f(x)) = 3(f(x)) - 2 \).

Step2: Replace f(x) with its expression

Now, substitute \( f(x) = x + 1 \) into the equation from Step 1. So we have \( g(f(x)) = 3(x + 1) - 2 \).

Step3: Simplify the expression

First, distribute the 3 in \( 3(x + 1) \) to get \( 3x + 3 \). Then subtract 2 from that result: \( 3x + 3 - 2 = 3x + 1 \).

Answer:

\( 3x + 1 \) (corresponding to the option with "3x+1")