# Inverse Equation

#### p4pri

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

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

Is this right?

Thanks.

#### allsmiles

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.

• p4pri

#### e^(i*pi)

MHF Hall of Honor
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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