Question

Help! Let f(x) be a function with domain [-3, ∞ ) and range (- ∞ , 2). If g(x) = f^-1 (x) (aka. g(x) is the inverse of f(x)), then what is the domain of g(x+4)-7 ?

Answer 1

`[-10,oo)` Range
`(-oo,6)` Domain

Explanation:

First of with inverse functions the domain and range switch so as `g(x)=f(x)^-1` the domain is `(-oo,2)` and the range `[-3,oo)`

We know that the whole of function `g(x)` has been shifted 7 downards so the range changes by the same amount `[-10,oo)`

As `g(x)` has moved 4 to the RHS so the domain moves 4 to the right `(-oo,6)`