Strictly Increasing Or Strictly Decreasing Function

To determine the nature of the function , we will investigate its properties in terms of evenness or oddness and monotonicity.

1. Check for Oddness:

A function is odd if for all . Calculate :

Note that . Therefore,

Since , the function is odd.

2. Check for Monotonicity:

To check whether the function is strictly increasing or decreasing, we calculate its derivative .

The derivative .

Therefore,

Observe that is positive for all . Thus, is strictly increasing for all .

Conclusively, the function is odd and is strictly increasing over .