Asked by Priya
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
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
Answers
Answered by
MathMate
Three steps to finding the inverse:
1. interchange x and y.
2. solve for y in terms of x.
3. evaluate f<sup>-1</sup>(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<sup>-1</sup>(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
1. interchange x and y.
2. solve for y in terms of x.
3. evaluate f<sup>-1</sup>(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<sup>-1</sup>(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
Answered by
Priya
THANKS ALOT... I GET IT NOW!!!!!!
Answered by
MathMate
You're welcome!
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