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

Last updated at Nov. 17, 2021 by Teachoo

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Question 14
The function f (x) = (4 β π₯^2)/(4π₯ βπ₯^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 β π₯^(2 ) )/(4π₯ β π₯^3 )
= (2^2 β π₯^(2 ) )/(π₯(4 β π₯^2))
= ((π β π)(π + π))/(π(π β π)(π + π))
If we cancel out (2 β π₯) and (2 + π₯)
Then, we have to assume that x β 2, and x β β2
So, our f(x) becomes
f(x) = π/π
This function is not defined for x = 0
Thus, f(x) is defined for all points except x = 0, 2, β2
β΄ f(x) is discontinuous at exactly 3 points
So, the correct answer is (C)

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