Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12
Example 20 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 13, 2021 by Teachoo
Transcript
Example 20 Show that the function f defined by f (x) = |1โ ๐ฅ + | ๐ฅ ||, where x is any real number is a continuousGiven ๐(๐ฅ) = |(1โ๐ฅ+|๐ฅ|)| Let ๐(๐) = 1โ๐ฅ+|๐ฅ| & ๐(๐) = |๐ฅ| Then , ๐๐๐(๐) = โ(๐(๐ฅ)) = โ(1โ๐ฅ+|๐ฅ|) = |(1โ๐ฅ+|๐ฅ|)| = ๐(๐) We know that, Modulus function is continuous โด ๐(๐) = |๐ฅ| is continuous Also, ๐(๐) = (๐โ๐)+|๐| Since (1โ๐ฅ) is a polynomial & every polynomial function is continuous โด (๐โ๐) is continuous Also, |๐| is also continuous Since Sum of two continuous function is also continuous Thus, ๐(๐ฅ) = 1โ๐ฅ+|๐ฅ| is continuous . Hence, ๐(๐ฅ) & โ(๐ฅ) are both continuous . We know that If two function of ๐(๐ฅ) & โ(๐ฅ) both continuous, then their composition ๐๐๐(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 9 years. He provides courses for Maths and Science at Teachoo.