Check sibling questions

The function f (x) = (4 - x^2)/(4x -x^3 ) is

(A) discontinuous at only one point

(B) discontinuous at exactly two points

(C) discontinuous at exactly three points

(D) none of these

This question is similar to Ex 5.1, 3 (c) - Chapter 5 Class 12 - Continuity and Differentiability

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Transcript

Question 14 The function f (x) = (4 βˆ’ π‘₯^2)/(4π‘₯ βˆ’π‘₯^3 ) is (A) discontinuous at only one point (B) discontinuous at exactly two points (C) discontinuous at exactly three points (D) none of these f(x) = (4 βˆ’ π‘₯^(2 ) )/(4π‘₯ βˆ’ π‘₯^3 ) = (2^2 βˆ’ π‘₯^(2 ) )/(π‘₯(4 βˆ’ π‘₯^2)) = ((𝟐 βˆ’ 𝒙)(𝟐 + 𝒙))/(𝒙(𝟐 βˆ’ 𝒙)(𝟐 + 𝒙)) If we cancel out (2 βˆ’ π‘₯) and (2 + π‘₯) Then, we have to assume that x β‰  2, and x β‰  βˆ’2 So, our f(x) becomes f(x) = 𝟏/𝒙 This function is not defined for x = 0 Thus, f(x) is defined for all points except x = 0, 2, βˆ’2 ∴ f(x) is discontinuous at exactly 3 points So, the correct answer is (C)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.