Let a be less than b which is less than c.
Suppose that f is continuous on [a,b], that g is continuous on [b,c], and that f(b)=g(b).
Define h on [a,c] by h(x):= f(x) for x in [a,b] and h(x):= g(x) for x in (b,c].
Prove that h is continuous on [a,c]
Let a be less than b which is less than c.
Suppose that f is continuous on [a,b], that g is continuous on [b,c], and that f(b)=g(b).
Define h on [a,c] by h(x):= f(x) for x in [a,b] and h(x):= g(x) for x in (b,c].
Prove that h is continuous on [a,c]
The only point in question is . Since is continuous,