`f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1` is continuous in the interval `[-1,1],` then `p` is equal to `-1` (b) `-1/2` (c) `1/2` (d) 1

Explanation

To determine the value of \( p \) such that the function

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