# 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 ?

Mar 26, 2018

$\left[- 10 , \infty\right)$ Range
$\left(- \infty , 6\right)$ Domain

#### Explanation:

First of with inverse functions the domain and range switch so as $g \left(x\right) = f {\left(x\right)}^{-} 1$ the domain is $\left(- \infty , 2\right)$ and the range $\left[- 3 , \infty\right)$

We know that the whole of function $g \left(x\right)$ has been shifted 7 downards so the range changes by the same amount $\left[- 10 , \infty\right)$

As $g \left(x\right)$ has moved 4 to the RHS so the domain moves 4 to the right $\left(- \infty , 6\right)$