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Question
Select the correct answer from the given alternatives:
f(x) = `(x^2 - 7x + 10)/(x^2 + 2x - 8)`, for x ∈ [– 6, – 3]
Options
f is discontinuous at x = 2
f is discontinuous at x = – 4
f is discontinuous at x = 0
is discontinuous at x = 2 and x = – 4
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Solution
f is discontinuous at x = – 4
Explanation;
f(x) = `(x^2 - 7x + 10)/(x^2 + 2x - 8)`; x ∈ [– 6, – 3]
= `(x^2 - 7x + 10)/((x + 4)(x - 2))`
Here f(x) is a rational function and is continuous everywhere except at the points Where the denominator becomes zero.
Here, denominator becomes zero when x = – 4 or x = 2
But x = 2 does not lie in the given interval
∴ x = – 4 is the point of discontinuity
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