Question

The function (f) is given by
`f(x)=e^(x-11) -8`

a) Find
`f^-1 (x)`

b) Write down the domain of
`f^-1 (x)`

Answer 1

`f(x)=e^(x-11)-8\to y=e^(x-11)-8\ \ \ \ |add\ 8\ to\ both\ sides\\\\e^(x-11)=y+8\\\\\ln e^(x-11)=\ln(y+8)\iff x-11=\ln(y+8)\ \ \ \ |add\ 11\ to\ both\ sides\\\\x=\ln(y+8)+11\\\\a)\ \boxed{f^(-1)(x)=\ln(x+8)+11}\\\\b)\ The\ domain\ of\ f^(-1)(x):\\\\x+8 > 0\to \boxed{x > -8\to x\in(-8;\ \infty)}`