Last updated at April 13, 2021 by
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Example 19 Show that the function defined by f (x) = sin (x2) is a continuous function.Given π(π₯) = sinβ‘(π₯^2 ) Let π(π) = sinβ‘π₯ & π(π) = π₯^2 Now, (π π π)(π) = g(β(π₯)) = π(π₯^2 ) = sinβ‘(π₯^2 ) = π(π) So, we can write π(π₯) = ππβ Here, π(π₯) = sinβ‘π₯ is continuous & β(π₯) = π₯^2 is continuous being a polynomial . We know that if two function π & β are continuous then their composition πππ is continuous Hence, ππβ(π₯) is continuous β΄ π(π) is continuous .
Continuity of composite functions
Continuity of composite functions
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