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If the function / satisfies the relation `f(x+y)+f(x-y)=2f(x),f(y)AAx , y in Ra n df(0)!=0` , then `f(x)i sa ne v e nfu n c t ion` `f(x)i sa nod dfu n c t ion` `Iff(2)=a ,t h e nf(-2)=a` `Iff(4)=b ,t h e nf(-4)=-b`

A

even

B

odd

C

periodic

D

none

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The correct Answer is:
A
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MOTION-FUNCTION-Exercise - 1 ( JEE Main)
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  2. It is given that f(x) is an even function and satisfy the relation f(x...

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  3. If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx ,...

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  4. Let f(x)=abs(x-1)+abs(x-2)+abs(x-3)+abs(x-4), then

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  5. Fundamental period of f(x)=sec(sin x) is

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  6. The period of sin(pi/4)x+cos(pi/2)x+cos(pi/3)x is

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  9. Which of the following is implicit functions -

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  10. I fy=f(x) satisfies the condition f(x+1/x)=x^2+1/(x^2)(x!=0) then f(x...

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  11. If f(x) = a(x^n +3), f(1) = 12, f(3) = 36, then f(2) is equal to

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  14. A function f : R->R satisfies the condition x^2f(x)+f(1-x)=2x-x^4. The...

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  15. Let f(x) = abs(x – 1). Then :

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  16. Let g(x) = 1 + x – [x] and f(x)={:{(-1,if,xlt0),(0,if, x=0),(1,if,x gt...

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  17. Let f: [0, 1] to [1, 2] defined as f(x) = 1 + x and g : [1, 2] to [0, ...

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  18. Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof)...

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  19. f(x) = |x-1|, f: R^+->R, g(x) = e^x, g:[-1,oo)->R. If the function fog...

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  20. Number of solution of 6 abscosx = x " in"[ 0.2pi] is

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