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 :

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 :

(3, 2)

(3, 1)

(2, 1)

$\left( {{1 \over 3},\,2} \right)$

Solution

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