I'm having trouble with this question and don't know how to solve it.

(10) Let f : R > R and M 6 [0,00). We say that f is \"Mbounded\" if Va: 6 R we have M S \"117) S M- (a) Prove that the function cos : R > R is 1-bounded. (You may only use the denition of cos given in the previous exercise.) (b) Determine if each of the following statements is true or false. If it's true, explain Why. If it's false explain Why not, or simply give an example demonstrating why it's false. (A correct choice of \"T/F\" with no explanation will not receive any credit.) (i) If f and g are M -bounded, then so is f + 9. (ii) If f is Mbounded, then f is M-bounded. (iii) If f is Mbounded, then f is M + l-bounded. (iv) For any f : 1R ) 1R, there exists and M > 0 so that f is M -bounded