# Original function with inverse

1. Sep 12, 2014

### MathewsMD

1. The problem statement, all variables and given/known data

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

2. Sep 12, 2014

### gopher_p

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.