Ex 5.1, 32 - Show that f(x) = |cos x| is continuous - Class 12 - Ex 5.1

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.1, 32 Show that the function defined by 𝑓 𝑥﷯= cos﷮𝑥﷯﷯ is a continuous function. 𝑓(𝑥) = cos﷮𝑥﷯﷯ Let 𝑔(𝑥) = 𝑥﷯ & ℎ 𝑥﷯ = cos﷮𝑥﷯ 𝑔𝑜ℎ 𝑥﷯ = g ℎ 𝑥﷯﷯ = 𝑔 cos﷮𝑥﷯﷯ = cos﷮𝑥﷯﷯ = 𝑓 𝑥﷯ Hence 𝑓 𝑥﷯ = 𝑔𝑜ℎ 𝑥﷯ We know that, h(x) = cos﷮𝑥﷯ is continuous & g (x) = 𝑥﷯ is continuous as it is a modulus function We know that If two function 𝑔 𝑥﷯ & ℎ 𝑥﷯ both continuous then their composition is also continuous ∴ 𝑔𝑜ℎ 𝑥﷯ is continuous Thus, 𝒇 𝒙﷯ is continuous for all real values.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.