Example 6 - Prove that identity function f(x) = x is continuous - Examples

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Example 6 Prove that the identity function on real numbers given by f (x) = x is continuous at every real number. Given ๐‘“ (๐‘ฅ) = ๐‘ฅ Let c be any real number. ๐‘“ is continuous at ๐‘ฅ=c if ๏ทlim๏ทฎxโ†’๐‘๏ทฏ ๐‘“๏ท๐‘ฅ๏ทฏ=๐‘“(๐‘) โˆด ๏ทlim๏ทฎxโ†’๐‘๏ทฏ ๐‘“๏ท๐‘ฅ๏ทฏ=๐‘“(๐‘) Hence, f is continuous at ๐‘ฅ =๐‘ โ‡’ f is continuous for x = c , where c โˆˆR โˆด f is continuous for every real number.

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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.