Multi-variable Composite Function

Question

If f(x)=x^4+8, g(x)=x-6, and h(x)=sqrt(x), then what would f(g(h(x))) equal?

Answer 1

First, let's find g(h(x)) by plugging in h(x) into g(x).

g(h(x)) = h(x) - 6

g(h(x)) = sqrt(x) - 6

Now, let's find f(g(h(x))) by plugging in g(h(x)) into f(x).

f(g(h(x))) = g(h(x))⁴ + 8

f(g(h(x))) = (sqrt(x) - 6)⁴ + 8