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Question
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
Solution
Given that f(x) = |sin x + cos x| at x = π
Put g(x) = sin x + cos x and h(x) = |x|
∴ h[g(x)] = h(sin x + cos x) = |sin x + cos x|
Now, g(x) = sin x + cos x is a continuous function since sin x and cos x are two continuous functions at x = π.
We know that every modulus function is a continuous function everywhere.
Hence, f(x) = |sin x + cos x| is continuous function at x = π.
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