Question

I am not sure how to do this problem...

Let g(x)=x-4. Find f(x) so that h(x)=(fog)(x)

h(x)=(x-4)^6

Answer 1

f(x) = x⁶

Explanation:

g(x) = x - 4

h(x) = (x - 4)⁶

h(x) = (g(x))⁶

h(x) = f(g(x)) = (g(x))⁶

Therefore,

f(x) = x⁶

Answer 2

f(x) = x^6

Explanation:

We see that h(x) is a composite function; basically, h(x) = f(g(x)), where instead of putting x into the function f(x), you put g(x) in for x.

We see that g(x) = x - 4 and that h(x) = f(g(x)) = (x - 4)^6. Let's replace (x - 4) in h(x) with g(x):

h(x) = f(g(x)) = (g(x))^6.

Ah, now we can see clearly that f(x) must be x^6 because remember that h(x) is simply putting g(x) in for x. If we change g(x) in (g(x))^6 to x, we get: x^6.

Thus, f(x) = x^6.

Hope this helps!