If f(x)={1+kx−1−kxx,for −1≤x<02x2+3x−2,for 0≤x≤1f(x) = \begin{cases} \frac{\sqrt{1+kx} - \sqrt{1-kx}}{x}, & \text{for } -1 \leq x < 0 \\ 2x^2 + 3x - 2, & \text{for } 0 \leq x \leq 1 \end{cases}…

Mathematics

Problem

If f(x)={1+kx−1−kxx,for −1≤x<02x2+3x−2,for 0≤x≤1f(x) = \begin{cases} \frac{\sqrt{1+kx} - \sqrt{1-kx}}{x}, & \text{for } -1 \leq x < 0 \\ 2x^2 + 3x - 2, & \text{for } 0 \leq x \leq 1 \end{cases} , is continuous at x=0x = 0 , then k=k = (a) -4 (b) -3 (c) -2 (d) -1

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