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`

Options

A. `-4`
B. `-3`
C. `-2`
D. `-1`

Answer

C

Explanation

We have ,
`f(x){:{((sqrt(1+kx)-sqrt(1-kx))/x,-1lexle0),(2x^(2)+3x-2 , 0le x le 1):}`
F(x) is continuous at x=0
` lim_(xto 0^(-)) f(x) = lim_( x to 0^(+)) f(x)`
` Rightarrow lim_(x to 0^(-)) (sqrt(1+kx) -sqrt(1-kx))/x`
`lim_(x to 0^(+) 2x^(2) + 3x-2`
`Rightarrow lim_(x to0^(-)) (1+kx-1 kx)/(xsqrt(1+kx) +sqrt(1+kx))=-2 `
`Rightarrow (2k)/2 =-2`
`Rightarrow k = -2 `