JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

f(x+y)=f(x) f(y) \forall x, y \in R

and

f(0) \neq 0

, then the function

\phi(x)=\frac{f(x)}{1+(f(x))^2}+\frac{\sin \left(\pi\left[x^2+x\right]\right.}{1+\sin (\cos x)}

(where [] denote the greatest integer function) is

View answer and explanation

Correct option: A

An even function

Option A (An even function) is correct because the function φ(x) is shown to satisfy φ(-x) = φ(x), indicating it is an even function.

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