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Continuity And Differentiability

Question

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Show that the function defined by f(x) = | cos x | is a continuous function.

Solution

Here f (x) = | cos x |
Let g(x) = | x | and h(x) = cos x
∴ (g o h) (x) = g (h(x)) = g(cos x) = | cos x |
Now f(x) = (g o h)(x) and g,h are both continuous functions.
∴ f is continuous function.

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