Example 20 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Jan. 3, 2020 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 continuous ๐(๐ฅ) = |(1โ๐ฅ+|๐ฅ|)| Let ๐(๐ฅ) = 1โ๐ฅ+|๐ฅ| & โ(๐ฅ) = |๐ฅ| Then , โ๐๐(๐ฅ) = โ(๐(๐ฅ)) = โ(1โ๐ฅ+|๐ฅ|) = |(1โ๐ฅ+|๐ฅ|)| Now โ(๐ฅ) = |๐ฅ| We know that Modulus function is continuous โด โ(๐ฅ) = |๐ฅ| is continuous ๐(๐ฅ) = (1โ๐ฅ)+|๐ฅ| Since (1โ๐ฅ) is a polynomial & every polynomial function is continuous โด (1โ๐ฅ) is continuous Also, |๐ฅ| is also continuous So, Sum of two continuous function is also continuous Thus, ๐(๐ฅ) = 1โ๐ฅ+|๐ฅ| is continuous . Hence, ๐(๐ฅ) & โ(๐ฅ) are both continuous . If two function of ๐(๐ฅ) & โ(๐ฅ) both continuous, then their composition โ๐๐(๐ฅ) 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.