Question

1. g(x) = 4x + 5

f(x) = 3x
find (g · f)(x)

Explanation:

Step1: Define product of functions

$(g \cdot f)(x) = g(x) \times f(x)$

Step2: Substitute given functions

$(g \cdot f)(x) = (4x + 5) \times 3x$

Step3: Distribute the term

$(g \cdot f)(x) = 4x \times 3x + 5 \times 3x$

Step4: Simplify each term

$(g \cdot f)(x) = 12x^2 + 15x$

Answer:

$12x^2 + 15x$