If the function h(x)=(x+9)^7 is expressed in the form f∘g with f(x)=x^7, then find the function g(x).

Question

I need help with this problem please!

Answer 1

If f(x) = x⁷ and (f•g)(x) = (x+9)⁷, there is a really slick way of getting g(x):

(f•g)(x) = f(g(x)) = (g + 9)⁷ = x⁷

only when g = x - 9

Hence g(x) = x - 9

Note that if the exponent had been a positive even number instead of an odd number (7), then there would have been two answers:

g(x) = x - 9 or

g(x) = -x - 9