Question

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

Answer 1

According to defintion of compostion of functions, we can get:


`(f\circ g)(x)=f(g(x))`

But we know, that:


`\displaystyle h(x)= (x^2)/(x^2+4)`

Our goal, is to express that function as a composition:


`(f\circ g)(x)=h(x) \Rightarrow f(g(x))=h(x)`

I.e:


`\displaystyle f(g(x))=(x^2)/(x^2+4)`

If
`\displaystyle f(y)= (y)/(y+4)` then
`g(x)=x^2`. Hence,
`\displaystyle h(x)=(f\circ g)(x)=f(g(x))= (g(x))/(g(x)+4) \Rightarrow f(g(x))=f(x^2)= (x^2)/(x^2+4)`