Ex 5.1, 31 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 3, 2020 by Teachoo

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Ex 5.1, 31 Show that the function defined by 𝑓(𝑥)=cos⁡(𝑥^2 ) is a continuous function. 𝑓(𝑥) = cos⁡(𝑥^2 ) Let 𝑔(𝑥) = cos⁡𝑥 & ℎ(𝑥) = 𝑥^2 𝑔𝑜ℎ(𝑥) = g(ℎ(𝑥)) = 𝑔(𝑥^2 ) = cos⁡(𝑥^2 ) = 𝑓(𝑥) So we can write 𝑓(𝑥) = 𝑔𝑜ℎ Here 𝑔(𝑥) = cos⁡𝑥 is continuous & ℎ(𝑥) = 𝑥^2 is continuous as it is a polynomial . We now that if two functions 𝑓(𝑥) & ℎ(𝑥) both continuous then their composition 𝑔𝑜ℎ(𝑥) is continuous ∴ Hence (𝑔𝑜ℎ) (𝑥) is continuous Thus, 𝒇(𝒙) is continuous .

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Chapter 5 Class 12 Continuity and Differentiability

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