COMEDK · Maths · 25. Continuity and Differentiability
\(\text { The number of points of discontinuity of the rational function } f(x)=\dfrac{x^2-3 x+2}{4 x-x^3}\)
- A 1
- B 2
- C 3
- D 5
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
The function is defined as \(f(x) = \dfrac{x^2 - 3x + 2}{4x - x^3}\). Factorizing the numerator and the denominator: Numerator: \(x^2 - 3x + 2 = (x - 1)(x - 2)\) Denominator: \(4x - x^3 = x(4 - x^2) = x(2 - x)(2 + x) = -x(x - 2)(x + 2)\) Thus,…
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