Question

Let f(x)=(4x^2-11)^3 and g(x)=4x^2-11. given that f(x)=(h^o g)(x), find h(x).

Answer 1

So, f(x) is a composite function. This means that g(x) is inside of h(x); in other words, you would substitute g(x) for x in h(x).

Something happened to g(x) (in the form of h(x)) to turn it into f(x). You should notice that f(x) is simply g(x) raised to the third power.

Therefore, h(x) = x^3

You can check this by working it backwards.

Start with: h(x) = x^3
Substitute: x = g(x) = 4x^2-11
Now you have: h(x) = (g(x))^3 = (4x^2-11)^3

Hope this helps!