Question

using the following equations, find g(f(x)): f(x) = 2x + 1 g(x) = x - 3 g(f(x)) = 2x + ?

Explanation:

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

To find \( g(f(x)) \), we substitute \( f(x) = 2x + 1 \) into \( g(x) \). So \( g(f(x)) = g(2x + 1) \).

Step2: Apply the rule of g(x)

Since \( g(x) = x - 3 \), replacing \( x \) with \( 2x + 1 \) gives \( g(2x + 1) = (2x + 1) - 3 \).

Step3: Simplify the expression

Simplify \( (2x + 1) - 3 \): \( 2x + 1 - 3 = 2x - 2 \). Comparing with \( 2x + [?] \), we see that the constant term is -2.

Answer:

-2