Continuity of composite functions

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

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Ex 5.1, 31 Show that the function defined by π(π₯)=cosβ‘(π₯^2 ) is a continuous function.π(π₯) = cosβ‘(π₯^2 ) Let π(π) = cosβ‘π₯ & π(π) = π₯^2 Now, πππ(π) = g(β(π₯)) = π(π₯^2 ) = cosβ‘(π₯^2 ) = π(π) Hence, π(π₯) = ππβ(π₯) We know that π(π) = cosβ‘π₯ is continuous as cos x is always continuous & π(π) = π₯^2 is continuous as it is a polynomial Hence, π(π₯) & β(π₯) are both continuous . We know that If two function of π(π₯) & β(π₯) both continuous, then their composition πππ(π) is also continuous Hence, π(π) is continuous .

#### Davneet Singh

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