The given function is:
[tex]f(x)=2x^3+2x^2-\frac{1}{x}[/tex]The last term of the function can be expressed as:
[tex]\begin{gathered} \frac{1}{x}=x^{-1} \\ \text{ So:} \\ f(x)=2x^3+2x^2-x^{-1} \end{gathered}[/tex]By definition, a polynomial function consists of:
As we can observe, the last term is raised to a negative integer power, -1 is not a whole number. Then this is not a polynomial function.
The answer is: No. There is an exponent on a variable x that is not a whole number. (the last option)
