Example 19 - Show that f(x) = sin (x2) is continuous - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 19 Show that the function defined by f (x) = sin (x2) is a continuous function. 𝑓(𝑥) = ﷐sin﷮﷐﷐𝑥﷮2﷯﷯﷯ Let 𝑔(𝑥) = ﷐sin﷮𝑥﷯ & ℎ﷐𝑥﷯ = ﷐𝑥﷮2﷯ ﷐𝑔 𝑜 ℎ﷯﷐𝑥﷯ = g﷐ℎ﷐𝑥﷯﷯ = 𝑔﷐﷐𝑥﷮2﷯﷯ = ﷐sin﷮﷐﷐𝑥﷮2﷯﷯﷯ = 𝑓﷐𝑥﷯ So we can write 𝑓﷐𝑥﷯ = 𝑔 𝑜 ℎ Here 𝑔﷐𝑥﷯ = ﷐sin﷮𝑥﷯ is continuous & ℎ﷐𝑥﷯ = ﷐𝑥﷮2﷯ is continuous being a polynomial . We know that if two function 𝑓 & ℎ are continuous then their composition 𝑔𝑜ℎ is continuous ⇒ Hence 𝑔𝑜ℎ﷐𝑥﷯ is continuous ⇒ 𝑓﷐𝑥﷯ is continuous .

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.