If the function h( x ) = ( x − 8 ) 4 is expressed in the form f ∘ g with f ( x ) = x 4 , then find the function g ( x ) .

Answer 1

These used to confuse me, too.

So, just like f(3) means that we replace x with 3 in our equation, f°g(x), aka f(g(x)), means that we replace x with g(x).

Since f(g(x)) = (x - 8)⁴ and f(x) = x⁴, you'll notice the difference is that x has been replaced with x - 8, so g(x) = x - 8.

Hope this helps!