Posted by **Priya** on Sunday, May 22, 2011 at 11:52am.

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 -
**MathMate**, Sunday, May 22, 2011 at 12:27pm
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 -
**Priya**, Sunday, May 22, 2011 at 12:42pm
THANKS ALOT... I GET IT NOW!!!!!!

- math :) -
**MathMate**, Sunday, May 22, 2011 at 3:32pm
You're welcome!

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