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Determine whether or not the definition of * On `R` , define * by `a*b=a+4b^2` gives a binary operation. In the event that * is not a binary operation give justification of this. Here, `Z^+` denotes the set of all non-negative integers.

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Let `a,b∈ R`
`implies a,4b^2in R`
`implies a+4b^2 inR`
`implies a`*`bin R`
Therefore,
`a`*`b inR,forall a,b inR`
Thus, * is a binary operation on R.
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