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If f(x) = {((sqrt(1+kx)-sqrt(1-kx))/(x),...

If `f(x) = {((sqrt(1+kx)-sqrt(1-kx))/(x), "if" -1 le x lt 0),((2x+k)/(x-1), "if" 0 le x le1):}`
is continuous at x = 0, then the value of k is

A

`(1)/(2)`

B

1

C

`-(3)/(2)`

D

`-(1)/(2)`

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The correct Answer is:
D
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