Question

How do I even start this? And how to i order the equation to solve

Answer 1

`f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}`

This is because

`h(x)=\sqrt x`

`g(x)=x-1`

`\implies g(h(x))=\sqrt x-1`

(that is, replace any instance of x in the definition of g with √x )

and

`f(x)=x^4+4`

`\implies f(\sqrt x-1)=(\sqrt x-1)^4+4`

(replace any x in f with √x - 1)

Also acceptable:

`(\sqrt x-1)^4+4=((\sqrt x)^4-4(\sqrt x)^3+6(\sqrt x)^2-4\sqrt x+1)+4`

`=\boxed{x^2-4x\sqrt x+6x-4\sqrt x+5}`

(assuming x is not negative)