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 \(\displaystyle y=x\)