Math Analysis
posted by Emily .
6. Prove that f(x) = (3/4)x^4 + 2 and g(x) = (4sqrt(108x216))/3 are inverses.
I know you solve it with composite functions f(g(x)) and g(f(x)), and I solved f(g(x)), but I can't seem to solve g(f(x)) to equal x, like it should. Can someone show me how to solve this? Thanks :)

The 4 in front of the sqrt is like the 4th root, like 3sqrt(... is the cubed root, etc.

You probably took a wrong turn in what was included inside the fourth root. Easy turn to miss. :)
f(x)=(3/4)x^4
g(x)= ((108((3/4)x^4 + 2)216)^(1/4))/3
= ((81x^4 + 216 216)^1/4) /3
= ((81x^4)^1/4) /3
= 81^(1/4)x^(1/4) /3
= 3 x / 3
= x 
Ohhhhh, I think I get it now. Thanks jim! :D :D