Ex 5.1, 33 - Examine that sin |x| is continuous - Class 12 CBSE - Continuity of composite functions

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.1, 33 Examine that sin⁡| 𝑥 | is a continuous function. 𝑓(𝑥) = sin ﷮ 𝑥﷯﷯ Let 𝑔(𝑥) = sin﷮𝑥﷯ & ℎ 𝑥﷯ = 𝑥﷯ 𝑔𝑜ℎ 𝑥﷯ = g ℎ 𝑥﷯﷯ = 𝑔 𝑥﷯﷯ = sin ﷮ 𝑥﷯﷯ = f (x) So we can write 𝑓 𝑥﷯ = 𝑔𝑜ℎ 𝑥﷯ We know that 𝑔 𝑥﷯ = sin﷮𝑥﷯ is continuous & ℎ 𝑥﷯ = 𝑥﷯ is continuous as modulus function is continuous We know that If two function 𝑔 𝑥﷯ & ℎ 𝑥﷯ both continuous then their composition 𝑔 𝑜 ℎ﷯ 𝑥﷯ is continuous ∴ 𝑔𝑜ℎ 𝑥﷯ is continuous Thus, 𝒇 𝒙﷯ is continuous for all real values.

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