CPM Homework Help : CALC Problem 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).

Hint 1:

Recall your answer to problem 2-27.

Hint 2:

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.

Hint 3:

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