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Let f(x) be a real valued function satis...

Let f(x) be a real valued function satisfying the functional equation f(x) + f(1 - x) = k for all `x in Q`, where k is a constant quantity. To evaluate the p and value at a point we use the relations to get the value of that function
Answer the following question based on above passage :
If `f(x) = 4^(X)/(4^X + 2)` where `x in Q` then
f(1/2007) + f(2/2007) +.....+f(2006/2007) equals to

A

1003

B

2006

C

2007

D

None of these

Text Solution

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The correct Answer is:
A
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PATHFINDER-FUNCTION-QUESTION BANK
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  5. Let f(x) be a real valued function satisfying the functional equation ...

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  7. Let (x) f1(x)-2f2(x) where f1(x) = "min"{x^2, |x|} "for"-1 le x le...

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  8. Let (x) f1(x)-2f2(x) where f1(x) = "min"{x^2, |x|} "for"-1 le x le...

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  9. Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(...

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  10. Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(...

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  11. Let f(x) = 1/2[f(xy) + f(x/y)] for x,y in R^+ such that f(1) = 0 f'(...

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  12. For all real values of x and y, 2f(x) cosy = f(x + y) + f(x - y) and b...

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  13. For all real values of x and y, 2f(x) cosy = f(x + y) + f(x - y) and b...

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  14. For all real values of x and y, 2f(x) cosy = f(x + y) + f(x - y) and b...

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  15. Match List - I with List-II

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  16. Match List - I with List-II

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  18. Match List - I with List-II

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