Question

Given f(x) = 4x+5 and g(x) = x² + x find (f∘g)(-5)

Answer 1

`(f\circ g)(-5) = f( g(-5)) = f( 20) = 85`

because

`g(-5) = (-5)^2 +(-5) = 25-5 =20`

and

`f(20) = 4(20)+5 = 80+5=85`

Answer 2

f(x) = 4x+5

g(x) = x² + x

From definition, (f∘g) is f(x) evauated at g(x)

(f∘g)(x) = f(g(x))

In this case:

(f∘g)(x) = 4(x² + x)+5 = 4x² + 4x + 5

At point x = -5:

(f∘g)(-5) = 4(-5)² + 4(-5) + 5 = 100 - 20 + 5 = 85