Inverse Equation

Apr 2009
16
0
What's the inverse of f(x)=e^(x-11)-8

I got y= ln(x+8)+11

Is this right?

Thanks.
 
May 2010
53
1
Altlanta GA
Hmmmmm... doing the math i got the same answer, so i supose it is right.


great job :)


if you want to show your work, i can dobble check to see if i did it the same way you did.
 
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e^(i*pi)

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Feb 2009
3,053
1,333
West Midlands, England
What's the inverse of f(x)=e^(x-11)-8

I got y= ln(x+8)+11

Is this right?

Thanks.
I get the same answer too. Although technically it is written as \(\displaystyle f^{-1}(x) = \ln(x+8)+11\)

Note that the domain of \(\displaystyle f^{-1}(x)\) is limited to \(\displaystyle x>-8\) because we cannot take the log of a negative number or 0 (well we can but then we get complex answers). The range is all the real numbers.


edit (more info): If you look at \(\displaystyle f(x)\) you may notice that the range is \(\displaystyle f(x) > -8\) and that the domain is all the real numbers. If you compare that to the range and domain of \(\displaystyle f^{-1}(x)\) you will see they've 'swapped' around. This is a property of all inverse functions. Furthermore functions and their inverses are reflections in the line \(\displaystyle y=x\)
 
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