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

Ex 5.1, 32 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Ex 5.1, 32 Show that the function defined by ๐‘“ (๐‘ฅ)= |cosโก๐‘ฅ | is a continuous function.๐‘“(๐‘ฅ) = |cosโก๐‘ฅ | Let ๐’ˆ(๐’™) = |๐‘ฅ| & ๐’‰(๐’™) = cosโก๐‘ฅ Now, ๐’ˆ๐’๐’‰(๐’™) = g(โ„Ž(๐‘ฅ)) = ๐‘”(cosโก๐‘ฅ ) = |cosโก๐‘ฅ | = ๐’‡(๐’™) Hence, ๐‘“(๐‘ฅ) = ๐‘”๐‘œโ„Ž(๐‘ฅ) We know that, ๐’‰(๐’™) = cosโก๐‘ฅ is continuous as cos is continuous & ๐’ˆ(๐’™) = |๐‘ฅ| is continuous as it is a modulus function Hence, ๐‘”(๐‘ฅ) & โ„Ž(๐‘ฅ) are both continuous . We know that If two function of ๐‘”(๐‘ฅ) & โ„Ž(๐‘ฅ) both continuous, then their composition ๐’ˆ๐’๐’‰(๐’™) is also continuous Hence, ๐’‡(๐’™) is continuous . .

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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.