Amanda wants to showcase her favorite function: $e(x) = 1 +\sqrt { x + 5 }$. She has built a function machine for her favorite function. Her brother Eric is always trying to mess up Amanda’s stuff, so he has created the inverse of $e(x)$, named it $e^{–1}(x)$, and programmed it into a second machine.

1. What is the domain of Amanda’s function machine?

   Hint (a):

   You can't square root negative numbers.

   Answer (a):

   $x\ge−5$

2. What is the equation for Eric’s function machine, $e^{–1}(x)$? What is the domain of Eric’s function machine?

   Hint: (b):

   What is the range of Amanda's function?

3. What happens if the two machines are stacked on top of each other? What is $e^{–1}(e(–4))$? Explain why this happens.

   Hint (c):

   A function and it's inverse undo each other.

4. If $e^{–1}(x)$ and $e(x)$ are graphed on the same set of axes, what would be true about the two graphs?

   Answer (d):

   They would be reflections of each other across the line $y=x$.

5. Sketch the two graphs on the same set of axes.

   Hint (e):

   Make sure that the graphs are inverses of each other.