The point(s), at which the function f given by 𝑓(𝑥) = {8(x/|x| ,x<0 -1, x≥0)┤ is continuous, is/are :
(a) 𝑥 ∈ R (b) 𝑥 = 0
(c) 𝑥 ∈ R – {0} (d) 𝑥 = −1 and 1
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
Last updated at May 29, 2023 by Teachoo
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Question 31 The point(s), at which the function f given by 𝑓(𝑥) = {■8(𝑥/|𝑥| ,𝑥<0@−1, 𝑥≥0)┤ is continuous, is/are : (a) 𝑥 ∈ R (b) 𝑥 = 0 (c) 𝑥 ∈ R – {0} (d) 𝑥 = −1 and 1 Given 𝑓(𝑥) = {■8(𝑥/|𝑥| ,𝑥<0@−1, 𝑥≥0)┤ Since |𝒙| = −x for x < 0 𝑓(𝑥) = {■8(𝑥/((−𝑥)),𝑥<0@−1, 𝑥≥0)┤ = {■8(−1. ,𝑥<0@−1, 𝑥≥0)┤ = −1 Since f(x) = −1 is a constant function And constant function is continuous for all real numbers So, the correct answer is (A)