Math Analysis

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6. Prove that f(x) = (3/4)x^4 + 2 and g(x) = (4sqrt(108x-216))/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 :)

  • Math Analysis -

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

  • Math Analysis -

    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

  • Math Analysis -

    Ohhhhh, I think I get it now. Thanks jim! :D :D

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