Question

given f(x) = 4x and g(x) = 7x + 3, find the following.
(a) fg(x)
(b) gf(x)
(a) fg(x) = \square (simplify your answer.)
(b) gf(x) = \square (simplify your answer.)

Explanation:

Step1: Find \( f[g(x)] \)

To find \( f[g(x)] \), we substitute \( g(x) \) into \( f(x) \). Given \( f(x) = 4x \) and \( g(x) = 7x + 3 \), we replace \( x \) in \( f(x) \) with \( 7x + 3 \). So, \( f[g(x)] = 4(7x + 3) \).
Expanding this, we get \( 4\times7x + 4\times3 = 28x + 12 \).

Step2: Find \( g[f(x)] \)

To find \( g[f(x)] \), we substitute \( f(x) \) into \( g(x) \). Replace \( x \) in \( g(x) = 7x + 3 \) with \( 4x \). So, \( g[f(x)] = 7(4x) + 3 \).
Simplifying this, we get \( 28x + 3 \).

Answer:

(a) \( f[g(x)] = 28x + 12 \)
(b) \( g[f(x)] = 28x + 3 \)