The function
f may be thought of as a composition g o h of the two functions g and h, where
g (x) = sin x and h(x) = x2 Since both g and h are continuous functions, by Theorem 2,
it can be deduced that f is a continuous function Example 20 Show that the function f defined by
f (x) = |1 – x + | x||,
where x is any real number, is a continuous function Solution Define g by g(x) = 1 – x + |x| and  h by h(x) = |x| for all real x