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JEE Math Practice Question

If the function f defined as $$f\left( x \right) = {1 \over x} - {{k - 1} \over {{e^{2x}} - 1}},x \ne 0,$$ is continuous at x = 0, then the ordered pair (k, f(0)) is equal to :

  1. A.(3, 2)
  2. B.(3, 1)
  3. C.(2, 1)
  4. D.$$\left( {{1 \over 3},\,2} \right)$$

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