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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

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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 . .

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