Question

Find (f ° g)(x) and (g ° f)(x)

f(x) = 7x-4, g(x)=5-3x

Answer 1

(f ◦ g)(x) = f(g(x))

substitute x = g(x) = 5 - 3x into f(x)

f(g(x)) = f(5 - 3x) = 7(5 - 3x) - 4 = 35 - 21x - 4 = 31 - 21x

(g ◦ f)(x) = g(f(x))

substitute x = f(x) into g(x)

g(f(x)) = 5 - 3(7x - 4) = 5 - 21x +12 = 17 - 21x