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Example 20 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at December 16, 2024 by Teachoo
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Chapter 5 Class 12 Continuity and Differentiability
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Example 20 Show that the function f defined by f (x) = |1ā š„ + | š„ ||, where x is any real number is a continuousGiven š(š„) = |(1āš„+|š„|)| Let š(š) = 1āš„+|š„| & š(š) = |š„| Then , ššš(š) = ā(š(š„)) = ā(1āš„+|š„|) = |(1āš„+|š„|)| = š(š) We know that, Modulus function is continuous ā“ š(š) = |š„| is continuous Also, š(š) = (šāš)+|š| Since (1āš„) is a polynomial & every polynomial function is continuous ā“ (šāš) is continuous Also, |š| is also continuous Since Sum of two continuous function is also continuous Thus, š(š„) = 1āš„+|š„| is continuous . Hence, š(š„) & ā(š„) are both continuous . We know that If two function of š(š„) & ā(š„) both continuous, then their composition ššš(š) is also continuous Hence, š(š) is continuous .
