A continuous function **f(x)** on \(R\rightarrow R\) satisfies the relation \[f(x)+f(2x+y)+5xy=f(3x-y)+2x^{2}+1\] where \(x,y€R\) then which of the options are correct?

**1.**f(x) is an even function.

**2.**f(x) is an odd function.

**3.**f(x) is many-one .

**4.**f(x) is one-one.

**5.**f(x) is neither even nor odd.

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