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Let `f(x)` be a function such that `: f(x - 1) + f(x + 1) = sqrt3 f(x),` for all `x epsilon R.` If `f(5) = 100,` then prove that the value of `sum_(r=o)^99 f(5 + 12r)` will be equal to `10000.`

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The correct Answer is:
10000
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FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-II
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  2. Let S be the set of non-negative integers. A function f: S to S is suc...

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  4. Consider two functions, f(x) and g(x) defined as under: f(x)={1+x^3,x ...

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  6. If the functions f, g and h are defined from the set of real numbers R...

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  7. Let f(x)=2cos^2x+sqrt(3)*sin2x+1. Then, its domain and range, so that ...

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  9. Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

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  11. Consider a real-valued function f(x) satisfying 2f(x y)=(f(x))^y+(f(y)...

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  12. If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all x,y in R and ...

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  13. Let f be a function from be set of positive integers to the set of rea...

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  14. Let f be a function from be set of positive integers to the set of rea...

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  15. If the range of the function f(x)=(x-1)/(p-x^2+1) does not contain any...

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  17. Let f(x) be a function such that : f(x - 1) + f(x + 1) = sqrt3 f(x), f...

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