A function is on action.

Algebra Level 3

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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