Original function with inverse

[MathewsMD]

Homework Statement

Can an inverse function be determined as either even or odd simply given its original function?

 

[gopher_p]

Homework Statement

Can an inverse function be determined as either even or odd simply given its original function?

Claim 1: If $f$ is even, then $f$ is not invertible.

Claim 2: If $f$ is odd and invertible, then $f^{-1}$ is odd.

The proofs are left as exercises for the reader.