Show that the function f (x) = |sin x + cos x| is continuous at x = p. Examine the differentiability of f, where f is defined by
f(x) = |sin x + cos x| at x = π
Now, put g(x) = sin x + cos x and h(x) = |x|
Hence, h[g(x)] = h(sin x + cos x) = |sin x + cos x|
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 common function is a continuous function everywhere.
Therefore, f(x) = |sin x + cos x| is continuous function at x = π.