is the below expression a polynomial?

Question

Let $f(t), g(t), h(t)\in \mathbb F_{q}[t]$. Let $F(t)=f(t)+g(t)h(t)^{2}$. Is $F(t)$ a polynomial in $\mathbb F_q[t]$ or is it a function?

Please help

Answer 1

It is both a polynomial and a function. We are given that $f(t),g(t),h(t)$ are polynomials, and the set of polynomials is closed under sums and products; therefore $F(t)$ is also a polynomial. And any polynomial can be considered a function as well, namely the function $F\colon \Bbb F_q\to\Bbb F_q$ given by $a \mapsto F(a)$.