Finding (fg)(x) and (fg)(7)

Question

Let f(x) = x²+5x and g(x) = 4 - x

Find (fg)(7)

Answer 1

f(x) = x^2 -5

g(x) = 4-x

just multiply the functions together

(fg)(x) = f(x)g(x)

= (x^2-5x)(4-x)

=x(x-5)(4-x)

(fg)(7) = 7(7-5)(4-7)= 7(2)(-3) = -52

or

f(7) =7^2-5(7)= 49-35= 14

g(7) = 4-7 =-3

(fg)(7) = 14(-3) = - 52

to be distinguished from a composite function

(fog)(x) = f(g(x))

(fog)(7) = f(g(7))

f(-3) = (-3)^2 -5(-3) =9+15 = 24

or

(fog)(x) = f(g(x)) = f(4-x) = (4-x)^2 -5(4-x)

(fog)(7) = (4-7)^2 -5(4-7) = (-3)^2 -5(-3) = 9+15 = 24