Chapter 4 - Section 4.1 - Inverse Functions - 4.1 Exercises - Page 394: 22

Part A: Polynomials functions of odd degree cannot be one to one. Part B: The polynomial function of odd degree may not be one to one.

Part A: Even functions have symmetry about the $y$ axis and fail the horizontal line test. They are not one to one. For example $f(x)=x^2$. $f(2)=4$ and $f(-2)=4$. This means the inverse would include points $(4,2)$ and $(4,-2) which would not be a function. Part B: The polynomial function of even degree cannot have an inverse. Polynomial functions of odd degree may not be one to one because an odd degree polynomial function may have an even function within it, and an even degree polynomial function is not a one to one function. So, the polynomial function of odd degree may not be one to one.