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 $\displaystyle y=x$