5. Let it] be a continuous function dened for all :1: I} [L For any say \".3- D, it satises flit!) = HI} + fly}; (a) Find l]. {b} Let a. be a positive real number. Prove that i. for any positive integer a, n\") = rie}; ii. for any positive rational number r, e") = ra]; iii. for any rational number 1': ar) = ra}. {c} It is known that for all real number I? there exists a sequence {$1.1} of rational numbers such that lim on = 1:. 11500 Show that for an},r I 2: I}1 ex} 2 Ia}, where a is a positive real constant. HenceJ prove that for any I 3} [L x} 2 clnz, where c is a constant