Check sibling questions

Question 14 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability (Term 1)

Last updated at March 29, 2023 by

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

Slide67.JPG

Slide68.JPG

Get live Maths 1-on-1 Classs - Class 6 to 12

Book 30 minute class for β‚Ή 499 β‚Ή 299

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)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.