Find the value of `k ,` for which `f(x)={(sqrt(1+k x)-\ sqrt(1-k x))/(x) "if",\ -1lt=x<0"(2x+1)/(x-1\ ) if"\ 0lt=x<1` is continuous at `x=0`

Explanation

To find the value of \( k \) for which the function

\[
f(x) =
\begin{cases}
\frac{\sqrt{1 + kx} - \sqrt{1 - kx}}{x} & \text{if } -1 < x < 0 \\
\frac{2x + 1}{x - 1} & \text{if } 0 < x < 1
\end{cases}
...