5. Let f (ac) be a continuous function dened for all a: > O. For any ac, y > 0, it satises f(03y) = f('L') +f(y)- (a) Find f(1). (b) Let a be a positive real number. Prove that i. for any positive integer n, f (a\") = n f (a); ii. for any positive rational number 7", f (GT) 2 r f (or); iii. for any rational number 7", ail") = r f (a). (c) It is known that for all real number .23, there exists a sequence {sun} of rational numbers such that lim ran = :10. Tia>00 Show that for any a: > 0, f (of) : a: f (a), Where a is a positive real constant. Hence, prove that for any a: > 0, f (at) : clnsc, where c is a constant. 6. Discuss the continuity of the function f(:c)= xcos(%)+sin(%) ifx70 0 ifx=0 7. The function f is continuous at z = 0 and is defined for -1