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If f(x) = cos|e^(2)| x + cos[-e^(2)]x wh...

If `f(x) = cos|e^(2)| x + cos[-e^(2)]x` where [x] stands for greatest integer function, then

A

`f(pi)=1`

B

`f(2pi)=1`

C

`f(pi//2)=1`

D

`f(pi//4)=1`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
  1. Suppose f:[-2, 2] rarr RR is defined by f(x)={{:(-1" for "-2 le x le 0...

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  2. If g[f(x)]=|sinx|, f[g(x)]=(sinsqrtx)^(2) then

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  3. If f(x) = cos|e^(2)| x + cos[-e^(2)]x where [x] stands for greatest in...

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  4. If f:RR rarr RR is defined by f(x)=x-[x] -(1)/(2)" for "x in RR, where...

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  5. Let g(x) =1+x-[x] and f(x) ={{:(-1, if, x lt 0),(0, if, x=0),(1, if, x...

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  6. If f: R to R and g: R to R are defined by f(x) =x-[x] and g(x) =[x] A...

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  7. If f(x)=[x], g(x)=x-[x] then which of the following functions is the z...

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  8. If f : R to R and g: R to R are given by f(x) =|x| and g(x) =[x] for e...

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  9. f(x) = {{:([x], if, -3 lt x le -1),(|x|, if, -1 lt x lt 1),(|[-x]|, if...

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  10. If f(x) is a polynomial fin x( gt0) satisfying the equation f(x)+f(1//...

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  11. If f(x) is a polynomial function such that f(x)f((1)/(x))=f(x)+f((1)/(...

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  12. If f:R to R is defined as f(x+y)=f(x)+f(y) AA x,y in R and f(1) = 7, f...

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  13. If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=

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  14. f: R to R is given by: f(x)= a^(x)/(a^(x) + sqrt(a)) AA x in R, then ...

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  15. If f(x) =((x-a)(x-b))/x and (f(x))/((x-y)(x-z))+ (f(y))/((x-z)(y-z)) +...

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  16. If 2f(x) -3f(1/x)=x^(2), x ne 0, then f(2)=

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  17. If f(0)=0, f(1)=1, f(2)=2 and f(x)=f(x-2)+f(x-3) " for " x=3, 4, 5, ……...

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  18. If f(x+y,x-y) =xy, then the arithmetic mean of f(x,y) and f(y,-x) is

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  19. Assertion (A) P:f(x) =logx^(3) and g(x) =3 log x are equal functions ...

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  20. Let f(x) =px^(2) + qx^(4) +r. Then for f to be on even function:

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