QuestionFind $f^{-1}(x)$, and state the domain and range of $f^{-1}(x)$ for $f(x)=\sqrt{12}(x+5)$.

Studdy Solution
The range of $f(x)$ is all real numbers greater than or equal to $-5\sqrt{12}$, because the smallest value $f(x)$ can take is $-5\sqrt{12}$ when $x=$. Therefore, the domain of $f^{-}(x)$ is all real numbers greater than or equal to $-5\sqrt{12}$.
So, the inverse function is $f^{-}(x)=\frac{x}{\sqrt{12}}-5$ with domain $x \geq -5\sqrt{12}$ and range $y$ is all real numbers.