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in Continuity and Differentiability by (31.3k points)
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If possible, redefine the function to make it continuous.

\(f(x) = \frac{x^2 + \sqrt{x} - 2}{(x^2 - 1)},\) for x < 1

f(x) = (x2 + x - 2)/(x2 - 1), for x < 1

\(=\frac{\sqrt{x + 3}-2}{\sqrt{2-x}-1},\) for x > 1

= 1, for x = 1; at x = 1.

1 Answer

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by (35.0k points)
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Best answer

f(x) = (x2 + x - 2)/(x2 - 1)

\(\therefore\) limit of the function does not exist.

\(\therefore\) f has irremovable discontinuity at x = 1

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