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Let f be a real vlaued fuction with doma...

Let f be a real vlaued fuction with domain R such that `f(x+1)+f(x-1)=sqrt(2)f(x)` for all ` x in R`, then ,

A

f(x) is a periodic function with period 8

B

f(x) is a periodic function with period 12

C

f(x) is a non-periodic function

D

f(x) is a periodic function with indeterminate period

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A
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OBJECTIVE RD SHARMA-REAL FUNCTIONS -Exercise
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  3. Let f be a real vlaued fuction with domain R such that f(x+1)+f(x-1)=s...

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  4. Let f be a real valued function with domain R satisfying f(x + k) =1+[...

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  5. The function f(x) given by f(x)=(sin 8x cos x-sin6x cos 3x)/(cos x cos...

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  6. If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and ...

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  7. Let f (x)=|x-2|+|x - 3|+|x-4| and g(x) = f(x+1). Then 1. g(x) is an ev...

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  8. If T(1) is the period of the function f(x)=e^(3(x-[x])) and T(2) is th...

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  9. If f(x)=sqrt(|3^(x)-3^(1)|-2) and g(x)=tan pi x, then domain of fog(x)...

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  10. Find the range of f(x)=sqrt(sin(cos x))+sqrt(cos(sin x)).

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  11. The domain of the function f(x)=(sin^(-1)(x-3))/(sqrt(9-x^(2))), is

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  12. If f: R to R and g: R to R are defined by f(x)=2x+3 and g(x)=x^(2)+7 ,...

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  13. Suppose f:[-2,2] to R is defined by f(x)={{:(-1 " for " -2 le x le 0...

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  14. If f:R->R and g:R->R is given by f(x) =|x| and g(x)=[x] for each x in ...

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  15. If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^...

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  16. The domain of the function f(x)=log(3+x)(x^2-1) is

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  17. Period of f(x) = sin 3x cos[3x]-cos 3x sin [3x] (where[] denotes the g...

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  18. Let f(x)=(1)/(x) and g(x)=(1)/(sqrt(x)). Then,

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  19. Domain of (sqrt(s^(2)-4x+3)+1) log(5)""((x)/(5))+(1)/(x)(sqrt(8x-2x^(2...

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  20. The period of the function f(x)=cos2pi{2x}+ sin2 pi {2x}, is ( ...

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