Composition and Inverse

Question

Given that f(x) = 4x−5 and g(x) = 2-x², calculate:

(a) f(g(0)) =

(b) g(f(0)) =

Answer 1

To find f(g(0)), first find g(0). g(0) = 2 - (0)² = 2. Once you get g(0), plug the result (2) into f(x): f(2) = 4(2) - 5 = 3 therefore f(g(0)) = 3

To find g(f(0)), first find f(0): f(0) = 4(0) - 5 = -5. Once you get f(0), plug the result (-5) into g(x): g(-5) = 2 - (-5)² = -23 therefore g(f(0)) = -23

Answer 2

We have that f(0)=-5 and g(0)=2. So

f(g(0))=f(2)=8-5=3 and

g(f(0))=g(-5)=2-25=-23.