If $$f(x)=$$$$sin$$⁡$$($$[x]π$$)x2+x+1$$, where [.] denotes the greatest integer

Correct option is 3f is a constant function

Questions

$If f (x) = \frac{\sin ([x] π)}{x^{2} + x + 1}, where [.] denotes the greatest integer$

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f is one-one

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detailed solution

Correct option is C

fx = sin xπx2+x+1 = 0x2+x+1 =0 since sinxπ =sin nπ =0 where x=n∈Z fx=0 is constant function

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If f(x)=sin⁡([x]π)x2+x+1, where [.] denotes the greatest integer

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$If f (x) = \frac{\sin ([x] π)}{x^{2} + x + 1}, where [.] denotes the greatest integer$