The point(s), at which the function f given by ๐‘“(๐‘ฅ) = {8(x/|x| ,x<0 -1, x≥0)โ”ค is continuous, is/are :

(a) ๐‘ฅ ∈ R                 (b) ๐‘ฅ = 0

(c) ๐‘ฅ ∈ R – {0}         (d) ๐‘ฅ = −1 and 1

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  1. Class 12
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Transcript

Question 31 The point(s), at which the function f given by ๐‘“(๐‘ฅ) = {โ– 8(๐‘ฅ/|๐‘ฅ| ,๐‘ฅ<0@โˆ’1, ๐‘ฅโ‰ฅ0)โ”ค is continuous, is/are : (a) ๐‘ฅ โˆˆ R (b) ๐‘ฅ = 0 (c) ๐‘ฅ โˆˆ R โ€“ {0} (d) ๐‘ฅ = โˆ’1 and 1 Given ๐‘“(๐‘ฅ) = {โ– 8(๐‘ฅ/|๐‘ฅ| ,๐‘ฅ<0@โˆ’1, ๐‘ฅโ‰ฅ0)โ”ค Since |๐’™| = โˆ’x for x < 0 ๐‘“(๐‘ฅ) = {โ– 8(๐‘ฅ/((โˆ’๐‘ฅ)),๐‘ฅ<0@โˆ’1, ๐‘ฅโ‰ฅ0)โ”ค = {โ– 8(โˆ’1. ,๐‘ฅ<0@โˆ’1, ๐‘ฅโ‰ฅ0)โ”ค = โˆ’1 Since f(x) = โˆ’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 10 years. He provides courses for Maths and Science at Teachoo.