5. Let f and g be two functions, and suppose that the number M is an upper bound for f (x) | on the interval [0, 10] and the number N is an upper bound for |g() | on the interval [0, 10]. For each of the following sentences, indicate clearly whether it is TRUE or FALSE. (A sentence is only true if it's always true, no matter which functions f and g we're talking about.) Write one complete English sentence to justify your answer. [Hint: Four of these are true, and four are false!] (a) M + 5 is an upper bound for If (x) + 5| on the interval [0, 10]. (b) M + 5 is an upper bound for If (x)| on the interval [0, 10]. (c) M is an upper bound for If (x) + 5| on the interval [0, 10]. (d) M - N is an upper bound for If (x) - g(x)| on the interval [0, 10]. 2 (e) 2M + N is an upper bound for |2f(x) - g(x)| on the interval [0, 10]. (f) M is an upper bound for If'(x) | on the interval [0, 10]. (g) M is an upper bound for If (x)| on the interval [3, 7]. (h) M/N is an upper bound for If (x)/g(x)| on the interval [0, 10]