The function f is defined by f (x) = e ^(x+2), where x is any real number. Find f ^-1(x) and state its domain.

y=e^x+2 , we want to make x the subject, x+2=ln(y), x=ln(y)-2, now that x is the subject, the inverse of the function can be found by swapping the x and the y. Therefore the inverse function is y=ln(x)+2, therefore f^-1(x)= ln(x) +2