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Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

The point(s), at which the function f given by 𝑓(π‘₯) = {8(x/|x| ,x<0 -1, xβ‰₯0)─ is continuous, is/are :

(a) π‘₯ ∈ RΒ  Β  Β  Β  Β  Β  Β  Β  Β (b) π‘₯ = 0

(c) π‘₯ ∈ R – {0}Β  Β  Β  Β  Β (d) π‘₯ = βˆ’1 and 1

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Transcript

Question 31 The point(s), at which the function f given by 𝑓(π‘₯) = {β– 8(π‘₯/|π‘₯| ,π‘₯<0@βˆ’1, π‘₯β‰₯0)─ is continuous, is/are : (a) π‘₯ ∈ R (b) π‘₯ = 0 (c) π‘₯ ∈ R – {0} (d) π‘₯ = βˆ’1 and 1 Given 𝑓(π‘₯) = {β– 8(π‘₯/|π‘₯| ,π‘₯<0@βˆ’1, π‘₯β‰₯0)─ Since |𝒙| = βˆ’x for x < 0 𝑓(π‘₯) = {β– 8(π‘₯/((βˆ’π‘₯)),π‘₯<0@βˆ’1, π‘₯β‰₯0)─ = {β– 8(βˆ’1. ,π‘₯<0@βˆ’1, π‘₯β‰₯0)─ = βˆ’1 Since f(x) = βˆ’1 is a constant function And constant function is continuous for all real numbers So, the correct answer is (A)

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Davneet Singh

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.