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Continuity of composite functions
Continuity of composite functions
Last updated at April 13, 2021 by Teachoo
Ex 5.1, 32 Show that the function defined by π (π₯)= |cosβ‘π₯ | is a continuous function.π(π₯) = |cosβ‘π₯ | Let π(π) = |π₯| & π(π) = cosβ‘π₯ Now, πππ(π) = g(β(π₯)) = π(cosβ‘π₯ ) = |cosβ‘π₯ | = π(π) Hence, π(π₯) = ππβ(π₯) We know that, π(π) = cosβ‘π₯ is continuous as cos is continuous & π(π) = |π₯| is continuous as it is a modulus function Hence, π(π₯) & β(π₯) are both continuous . We know that If two function of π(π₯) & β(π₯) both continuous, then their composition πππ(π) is also continuous Hence, π(π) is continuous . .