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math

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what is inverse of this funtion
f(x)=(1 / 3)^x?
I think the answer is

f-1(x)= log base 1/3 of x, but i know im wrong... please help!!! THANK YOU

  • math -

    Three steps to finding the inverse:
    1. interchange x and y.
    2. solve for y in terms of x.
    3. evaluate f-1(f(x)) to verify that it gives x as the result.

    0. y=(1/3)^x
    1. x=(1/3)^y
    2. log(x)=ylog(1/3)
    => y=log(x)/log(1/3)=-log(x)/log(3)
    or
    f-1(x)=-log(x)/log(3)
    3.
    y(f(x))
    =y((1/3)^x)
    =-log((1/3)^x)/(log(3)
    =-xlog(1/3)/log(3)
    =x OK

  • math -

    THANKS ALOT... I GET IT NOW!!!!!!

  • math :) -

    You're welcome!

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