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If f(x)={(sqrt(1+k x)-sqrt(1-k x))/x for...

If `f(x)={(sqrt(1+k x)-sqrt(1-k x))/x` for `1 le x< 0 and 2x^2+3x-2 for0 le x le 1` is continuous at `x-0` then `k`

A

`-4`

B

`-3`

C

`-2`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
`LHL=lim_(x to 0^(-))(sqrt(1+kx)-sqrt(1-kx))/(x)xx(sqrt(kx)+sqrt(1-kx))/(sqrt(1+kx)+sqrt(1-kx))`
`=lim_(x to 0^(-))(2kx)/(x(sqrt(1+kx)+sqrt(1-kx)))=k`
`RHL=lim_(x to 0^(+))(2x^(2)+3x-2)= -2`
Since, it is given that f(x) is continuous.
`therefore LHL=RHL`
`rArr k = -2`
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