Consider the following function.
$f(x) = \sqrt{x - 7}$, $x > 7$
What is the domain of $f$? (Enter your answer using interval notation.)
Is $f$ continuous on this domain?
Yes
No
Find $f'(x)$.
$f'(x) = $
Does $f$ have an inverse function?
Yes
No
Consider the real number $a = 3$. For what value of $x$ does $f(x) = 3$? (If an answer does not exist, enter DNE.)
$x = $
Determine the value of $f^{-1}(3)$, if it exists. (If an answer does not exist, enter DNE.)
$f^{-1}(3) = $
Use the function $f$ and the real number $a = 3$ to find $(f^{-1})'(3)$, if it exists. (If an answer does not exist, enter DNE.)
$(f^{-1})'(3) = $