Question

Find (H*F) (x)
if h(x)=5-x and f(x)=3x+2
Please explain

Answer 1

h(x) = 5 - x
Domain: Df = R

f(x) = 3x + 2
Domain: Df = R

Dh = Df therefore (h·f)(x) = h(x) · f(x)

(h·f)(x) = (5 - x)(3x + 2) = 5(3x + 2) - x(3x + 2) = 5·3x + 5·2 - x·3x - x·2

= 15x + 10 - 3x² - 2x = -3x² + 13x + 10