(W If f(x) = cos x + here [.] denot...
Question

# (W If f(x) = cos x + here [.] denotes the greatest integer function), then f(x) is (A) even (B) odd (C) even and odd simultaneously (D) none of these

JEE/Engineering Exams
Maths
Solution
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( f(x)=cos |x|+left[left|frac{sin x}{2}right|right] ) ( therefore f(-x)=cos |-x|+left.[sin (-x)]_{2}right|_{-f(-x)=f(x)} mid=f(x) ) ( f(-x)=cos |x|+left[left|frac{sin x}{2}right|right]=f(x) ) ( therefore quad: f(-x) ) is even ( (A) ) even.