The function f is defined as f(x) = e^(x-4). Find the inverse of f and state its domain.

Firstly, we let y=f(x) so that y=e^x-4. The aim of this question is to find the inverse of y=f(x), and in order to do that, we must rearrange the question so that x becomes the subject of the equation, which will be our inverse function of f. The first step is to eliminate the exponential by applying the log_e function to each side of the equation, as log_e(e^x) = x. Therefore, we get: log_e(y)=log_e(e^x-4), log_e(y)=x-4, x=log_e(y)+4. Now we have x the subject of the equation, the inverse is log_e(y)+4. The question is asking about the inverse of f(x) so we replace y with x and obtain f^-1(x) = log_e(x) + 4.The domain of f^-1(x) is the set of input values that f(x) accepts, so we must find those values. We know that the domain of log(x) only takes values above 0, therefore the domain of f^-1(x) is 0 < x < +infinity.