Most Important Selected Qs for JEE AdvancedMathematicsFunctions

Let f: R [-1,1] be defined as f(x)= ( x) then which of the following is/are correct?

Options

Af is periodic with fundamental period 2
Brange of f=[ 1,1]
C_ x / 2 (f ( 2 -x )+f ( 2 +x ) )=2
Df is neither even nor odd function

Correct answer

C. _ x / 2 (f ( 2 -x )+f ( 2 +x ) )=2

Step-by-step solution

aligned & (A)f(x)= ( x) & As f(x+ )= ( ( +x))= (- x)= ( x)=f(x) & (B) As -1 x 1 & 1 ( x) 1 & (C) _ x / 2 [f ( 2 -x )+f ( 2 +x ) ] & = _ x / 2 2 ( x)=2 aligned (D) Clearly f(x) is even function

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