Check sibling questions

Example 20 - Show that function f(x) = |1 - x + |x|| is continous

Example 20 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Example 20 - Chapter 5 Class 12 Continuity and Differentiability - Part 3


Transcript

Example 20 Show that the function f defined by f (x) = |1βˆ’ π‘₯ + | π‘₯ ||, where x is any real number is a continuousGiven 𝑓(π‘₯) = |(1βˆ’π‘₯+|π‘₯|)| Let π’ˆ(𝒙) = 1βˆ’π‘₯+|π‘₯| & 𝒉(𝒙) = |π‘₯| Then , π’‰π’π’ˆ(𝒙) = β„Ž(𝑔(π‘₯)) = β„Ž(1βˆ’π‘₯+|π‘₯|) = |(1βˆ’π‘₯+|π‘₯|)| = 𝒇(𝒙) We know that, Modulus function is continuous ∴ 𝒉(𝒙) = |π‘₯| is continuous Also, π’ˆ(𝒙) = (πŸβˆ’π’™)+|𝒙| Since (1βˆ’π‘₯) is a polynomial & every polynomial function is continuous ∴ (πŸβˆ’π’™) is continuous Also, |𝒙| is also continuous Since Sum of two continuous function is also continuous Thus, 𝑔(π‘₯) = 1βˆ’π‘₯+|π‘₯| is continuous . Hence, 𝑔(π‘₯) & β„Ž(π‘₯) are both continuous . We know that If two function of 𝑔(π‘₯) & β„Ž(π‘₯) both continuous, then their composition π’‰π’π’ˆ(𝒙) is also continuous Hence, 𝒇(𝒙) 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 12 years. He provides courses for Maths and Science at Teachoo.