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Question
The function f(x) = `(4 - x^2)/(4x - x^3)` is ______.
Options
Discontinuous at only one point
Discontinuous at exactly two points
Discontinuous at exactly three points
None of these
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Solution
The function f(x) = `(4 - x^2)/(4x - x^3)` is discontinuous at exactly three points.
Explanation:
Given that: f(x) = `(4 - x^2)/(4x - x^3)`
For discontinuous function
4x – x3 = 0
⇒ x(4 – x2) = 0
⇒ x(2 – x)(2 + x) = 0
⇒ x = 0, x = – 2, x = 2
Hence, the given function is discontinuous exactly at three points.
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