The point(s), at which the function f given by ๐(๐ฅ) = {8(x/|x| ,x<0 -1, x≥0)โค is continuous, is/are :
(a) ๐ฅ ∈ R (b) ๐ฅ = 0
(c) ๐ฅ ∈ R – {0} (d) ๐ฅ = −1 and 1
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Last updated at Sept. 4, 2021 by Teachoo
Transcript
Question 31 The point(s), at which the function f given by ๐(๐ฅ) = {โ 8(๐ฅ/|๐ฅ| ,๐ฅ<0@โ1, ๐ฅโฅ0)โค is continuous, is/are : (a) ๐ฅ โ R (b) ๐ฅ = 0 (c) ๐ฅ โ R โ {0} (d) ๐ฅ = โ1 and 1 Given ๐(๐ฅ) = {โ 8(๐ฅ/|๐ฅ| ,๐ฅ<0@โ1, ๐ฅโฅ0)โค Since |๐| = โx for x < 0 ๐(๐ฅ) = {โ 8(๐ฅ/((โ๐ฅ)),๐ฅ<0@โ1, ๐ฅโฅ0)โค = {โ 8(โ1. ,๐ฅ<0@โ1, ๐ฅโฅ0)โค = โ1 Since f(x) = โ1 is a constant function And constant function is continuous for all real numbers So, the correct answer is (A)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
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