[Math] Example of continuous increasing and decreasing functions that don’t intersect.

Question

I am looking to describe two continuous functions. One of them is strictly increasing on the real line and one of them is strictly decreasing on the real line. I want to describe these functions in terms of non-exponential and non-trigonometric elementary functions.

I have this constraint because in my real analysis course these functions have not been introduced yet.

I wrote the problem off as easy but now I realize that I would not know how to solve it.

Answer 1

Consider $$f(x)=\frac{x}{1+|x|}$$

and move it up and down, and reflect it, to get two continuous monotone functions that don't cross each other.