I've been trying to solve this for a few days and am having no luck and need some help please.
f(x)=sqrt x g(x)=x^2 and h(x)= x+2. Write q(x)=sqrt x^2+4x+4 as a composition of f, g, h.
We start with
q(x) =
Since f(x) = we can write as f(x²+4x+4)
q(x) = f(x²+4x+4)
We factor the trinomial:
q(x) = f((x+2)(x+2))
We write that product as the square of a binomial:
q(x) = f((x+2)²)
Since g(x)=x², we can write (x+2)² as g(x+2)
q(x) = f(g(x+2))
Since h(x) = x+2, we can write g(x+2) as g(h(x))
q(x) = f(g(h(x)))
and we can write that using the composition notation as
q(x) = f∘(g∘h(x))
And maybe the parentheses can be eliminated and we can just
write
q(x) = f∘g∘h(x)
Edwin