Ex 5.1, 31 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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) = cos𝑥 & 𝒉(𝒙) = 𝑥^2 Now, 𝒈𝒐𝒉(𝒙) = g(ℎ(𝑥)) = 𝑔(𝑥^2 ) = cos(𝑥^2 ) = 𝒇(𝒙) Hence, 𝑓(𝑥) = 𝑔𝑜ℎ(𝑥) We know that 𝒈(𝒙) = cos𝑥 is continuous as cos x is always continuous & 𝒉(𝒙) = 𝑥^2 is continuous as it is a polynomial Hence, 𝑔(𝑥) & ℎ(𝑥) are both continuous . We know that If two function of 𝑔(𝑥) & ℎ(𝑥) both continuous, then their composition 𝒈𝒐𝒉(𝒙) is also continuous Hence, 𝒇(𝒙) is continuous .
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