(3) If [a, b] is a closed interval with -co 0 for each j = 0, . . . , n -1, and if f : [a, b] - R is a real function we write Aff = f (cj+1) - f (x;). We say that f is of bounded variation in a, b if n-1 Vy (a, b) = sup PEP([ ,]) 1=0 where V (a, b) is called the total variation of f on [a, b]. Prove that if g and h are two monotonic increasing functions on [a, b], then f (x) = g (x) - h (r) is a function of bounded variation on [a, b]