Question 12
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
f(x) = (4 − 𝑥^(2 ) )/(4𝑥 − 𝑥^3 )
= (2^2 − 𝑥^(2 ) )/(𝑥(4 − 𝑥^2))
= ((𝟐 − 𝒙)(𝟐 + 𝒙))/(𝒙(𝟐 − 𝒙)(𝟐 + 𝒙))
If we cancel out (2 − 𝑥) and (2 + 𝑥)
Then, we have to assume that x ≠ 2, and x ≠ −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, −2
∴ f(x) is discontinuous at exactly 3 points
So, the correct answer is (C)

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.

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