Question

If `h(x)=f(g(x))` how do you determine f(x) and g(x) given `h(x)=abs(x^2-4x+5)`?

Answer 1

Just one solution from many : g = (x-2) and f = x^2+1

Explanation:

As `x^2-4x+5=(x-2)^2+1 >=1`,

`h(x)=|x^2-4x+5|=x^2-4x+5`

Just one solution from many :

`g = (x-2) and f = x^2+1.`

`f(g)=g^2+1=(x-2)^2+1=h`