Express the following function, as a composition of two functions f and g. h(x)=x^2/(x^2 +4)

Question

(x² +4) is the denominator

Answer 1

a composition function h(x)=g(x)ºf(x)=g(f(x)) ... so you plug in the function after the "º" symbol in to the previous one. 

 

One that would work for this would be f(x)=x² and g(x)=x/(x+4)  

 

g(f(x))= (x²)/((x²)+4)

Answer 2

One answer could be

 

h(x) = (f ο g)(x) = f(g(x))

 

where

 

g(x) = x/√(x² + 4)

f(x) = x²

 

Then 

 

f(g(x)) = g(x)² = [x/√(x² + 4)]² = x²/(x² + 4) = h(x)