Show that the function $f(x) = |\sin x + \cos x|$ is continuous at $x = \pi$.

We have, $f(x) = |\sin x + \cos x|$ at $x = \pi$

Let $g(x) = \sin x + \cos x$
and $h(x) = |x|$

therefore,$hog(x) = h[g(x)]$

$= h(\sin x + \cos x)$

$= |\sin x + \cos x|$

As we know that sum of two continuous function is a continuous function and $g(x) = \sin x + \cos x$ is a continuous function as it is forming with addition of two continuous functions $\sin x$ and $\cos x$.

Also, $h(x) = |x|$ is also a continuous function. Since, we know that composite functions of two continuous functions is also a continuous function.

Therefore we can say that $f(x) = |\sin x + \cos x|$ is a continuous function everywhere.

Therefore we can say that $f(x)$ is continuous at $x = \pi$.