Inverse of a function exists if these conditions are met?

Question

Suppose a function's domain and range are restricted to the nonnegative reals. Are there any functions in this set which don't have inverses?

Constraints

1. The only parabolic form the function can take is of the form $x^{2n}$ i.e if $P(x) = x^{2n} +Q(x)$ then $Q(x)$ is a zero polynomial.
2. The function is not of the form $\frac{k}{x^{2n}} + c$
3. The function is neither trigonometric, nor exponential, nor logarithmic.