### Home > CALC > Chapter 2 > Lesson 2.1.3 > Problem2-38

2-38.

Is the inverse of an odd function also a function? Is the inverse also odd? How do you know? Include a statement to support your answer and sketch a graph of an example. Investigate this using the Draw Inverse eTool (Desmos).

Recall your answer to problem 2-27.

The vertical line test: $f$ is a function if each $x$-value has exactly one out $y$-value.
The horizontal line test: The inverse of $f$ is a function if each $y$-value has exactly one x-value.

Consider common even and odd functions:
common even functions: $x^2$, $x^4$, $x^6$, $|x|$, $\text{cos}x$
common odd functions: $x$, $x^3$, $x^5$, $\text{sin}x$

Use the eTool below to explore.
Click on the link to the right to view the full version of the eTool. Draw Inverse eTool