Question

1. find f(g(x)) when f(x) = 4x + 10 and g(x) = 4x - 1

a) f(g(x)) = 16x + 6 b) f(g(x) = 16x + 14 c) f(g(x)) = 16x + 9
d) f(g(x)) = 16x + 39

Explanation:

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

To find \( f(g(x)) \), we substitute \( g(x) = 4x - 1 \) into \( f(x) \). So \( f(g(x)) = f(4x - 1) \).

Step2: Apply f(x) formula

Since \( f(x) = 4x + 10 \), replace \( x \) with \( 4x - 1 \):
\( f(4x - 1) = 4(4x - 1) + 10 \).

Step3: Simplify the expression

First, distribute the 4: \( 4 \times 4x - 4 \times 1 + 10 = 16x - 4 + 10 \).
Then, combine like terms: \( 16x + ( - 4 + 10) = 16x + 6 \).

Answer:

a) \( f(g(x)) = 16x + 6 \)