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If f(x) satisfies the relation f(x)+f(x+...

If `f(x)` satisfies the relation `f(x)+f(x+4)=f(x+2)+f(x+6)` for all`x ,` then prove that `f(x)` is periodic and find its period.

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ARIHANT MATHS-FUNCTIONS-Exercise (Single Integer Answer Type Questions)
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  3. Let f(n) denotes the square of the sum of the digits of natural number...

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  4. If [sinx]+[x/(2pi)]+[(2x)/(5pi)]=(9x)/(10pi), where [*] denotes the gr...

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  5. The number of integral solutions of 1/x+1/y=1/6 " with " x le y " is "...

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  6. If f(x) is a polynominal of degree 4 with leading coefficient '1' sati...

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  7. If a+b = 3- cos 4 theta and a-b =4 sin 2theta, then ab is always less ...

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  8. Let 'n' be the number of elements in the domain set of the function f(...

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  9. Let f(x) be a function such that , f(x-1)+f(c+1)=sqrt(3)f(x), forall x...

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  10. If 2f(x)=f(x y)+f(x/y) for all positive values of x and y,f(1)=0 and f...

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  11. Let f be a function from the set of positive integers to the set of re...

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  12. If f(x)=(x^(4)+x^(2)+1)/(x^(2)-x+1), the value of f(omega^(n)) (where ...

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  13. If f^2(x)*f((1-x)/(1+x))=x^3, [x!=-1,1 and f(x)!=0], then find |[f(-2)...

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  14. An odd function is symmetric about the vertical line x=a ,(a >0),a n d...

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  15. L e t(e^x-e^(-x))/(e^x+e^(-x))=lnsqrt((1+x)/(1-x)),then find x.

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  16. If x is real, the maximum value of (3x^(2)+9x+17)/(3x^(2)+9x+7) is (...

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  17. If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for allx , th...

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  18. A non-zero function f (x) is symmetrical about the line y=x then the v...

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  19. Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1). If the range of this ...

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  20. Let f(x)be a monotic ploynomial of degree (2m-1) where m in N Then the...

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