### Home > INT3 > Chapter 5 > Lesson 5.2.2 > Problem5-71

5-71.

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?

You can't square root negative numbers.

$x\ge−5$

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

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.

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?

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

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

Make sure that the graphs are inverses of each other.