what is inverse of this funtion

Question

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

Answer 1

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

Answer 2

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

Answer 3

You're welcome!