Example 19 Show that the function defined by f(x) = sin (x2) is a continuous function Solution Observe that the function is defined for every real number 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