QuestionFind the inverse function $f^{-1}(x)$ and its domain and range for $f(x)=\sqrt{x}+4$.

Studdy Solution
Finally, we find the range of $f^{-1}(x)$. The range of a function is the set of all possible output values (y-values).For the function $f^{-1}(x)=(x-4)^2$, the output can be any non-negative real number because a square of any real number is always non-negative.
So, the range of $f^{-1}(x)$ is $[0, \infty)$.
The inverse function is $f^{-1}(x)=(x-4)^2$, the domain of $f^{-1}(x)$ is $(-\infty, \infty)$, and the range of $f^{-1}(x)$ is $[0, \infty)$.