Show that $*: R \times R \rightarrow R$ given by $(a, b) \rightarrow a+4 b^{2}$ is a binary operation.

(N/A) binary operation $*$ on a set $R$ is a function $*: R \times R \rightarrow R$.
For any pair $(a, b) \in R \times R$,the expression $a + 4b^{2}$ is a well-defined real number because $a$ and $b$ are real numbers,and the set of real numbers $R$ is closed under addition and multiplication.
Since for every pair $(a, b) \in R \times R$,there exists a unique element $a + 4b^{2} \in R$,the operation $*$ is a binary operation on $R$.