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The function f(x) = { (sqrt(1+px) - sqrt(1-px)) / x for -1 <= x < 0; (2x+1)/(x-2) for 0 <= x <= 1 } is continuous on [-1, 1]. What is the value of p?

1. -1
2. 1
3. 1/2
4. -1/2

Correct answer: -1/2

Solution

At x=0: f(0) = (2*0+1)/(0-2) = 1/(-2) = -1/2. LHL: multiply numerator and denominator by (sqrt(1+px)+sqrt(1-px)): [(1+px)-(1-px)] / [x*(sqrt(1+px)+sqrt(1-px))] = 2px / [x*(sqrt(1+px)+sqrt(1-px))] = 2p/(sqrt(1+p*0)+sqrt(1-p*0)) = 2p/2 = p. Setting p = -1/2.

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