Check sibling questions

Ex 5.1, 32 - Show that f(x) = |cos x| is continuous - Class 12

Ex 5.1, 32 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Ex 5.1, 32 Show that the function defined by 𝑓 (π‘₯)= |cos⁑π‘₯ | is a continuous function.𝑓(π‘₯) = |cos⁑π‘₯ | Let π’ˆ(𝒙) = |π‘₯| & 𝒉(𝒙) = cos⁑π‘₯ Now, π’ˆπ’π’‰(𝒙) = g(β„Ž(π‘₯)) = 𝑔(cos⁑π‘₯ ) = |cos⁑π‘₯ | = 𝒇(𝒙) Hence, 𝑓(π‘₯) = π‘”π‘œβ„Ž(π‘₯) We know that, 𝒉(𝒙) = cos⁑π‘₯ is continuous as cos is continuous & π’ˆ(𝒙) = |π‘₯| is continuous as it is a modulus function 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’ˆπ’π’‰(𝒙) is also continuous Hence, 𝒇(𝒙) is continuous . .

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.