Example 20 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Nov. 19, 2019 by Teachoo
Transcript
Example 20 Show that the function f defined by f (x) = |1− 𝑥 + | 𝑥 ||, where x is any real number is a continuous 𝑓𝑥 = 1−𝑥+𝑥 Let 𝑔(𝑥) = 1−𝑥+𝑥 & ℎ(𝑥) = 𝑥 Then ℎ 𝑜 𝑔𝑥 = ℎ𝑔𝑥 = ℎ1−𝑥+𝑥 = 1−𝑥+𝑥 Now ℎ(𝑥) = 𝑥 We know that Modulus function is continuous ⇒ ℎ(𝑥) = 𝑥 is continuous 𝑔(𝑥) = 1−𝑥+𝑥 Since 1−𝑥 is a polynomial & we know that every polynomial function is continuous ⇒ 1−𝑥 is continuous & ℎ(𝑥) = 𝑥 is also continuous We know that Sum of two continuous function is also continuous 𝑔𝑥 = 1−𝑥+𝑥 is continuous . Hence 𝑔𝑥 & ℎ𝑥 are both continuous . If two function of 𝑔𝑥 & ℎ𝑥 both continuous then their composition ℎ 𝑜 𝑔𝑥 is also continuous Hence 𝒇𝒙 is continuous .
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About the Author
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.