Question

I need help figuring out b. and how to set it up.

Answer 1

Answer:

$[5, +\infty>$

Step-by-step explanation:

The domain of $f^{-1}$ is the range of $f$, so we have to find a range of

The domain of $f$ is a set of all real numbers x, such that

                                          $x-2 \geq 0 \Rightarrow x\geq 2$

Therefore, the domain of $f$ is the set  $[2,\infty>$.

$f$ is an increasing function, so we can insert the smallest and the greatest value of the domain and we will obtain the smallest and the greatest value of the range of

So, we insert 2 into $f$ and that will be the smallest value in the range of

                          $f(2)=\sqrt{2-2}+5 =0+5=5$

If we insert an $\infty$ into the $f$:

$\lim_{x \to \infty} f(x) = \lim_{x \to \infty} \sqrt{x-2}+5 = \infty$

So the range of $f$, that is also a domain of $f^{-1}$ is:

                                          $[5, +\infty>$