Let f: r>r be a function satisfying s(x+y)= f(x)f (v), vx,y e r and lim f(x)=1. x0 which of the following are necessarily true? (a) fis strictly increasing (b)

Let f: R>R be a function satisfying S(x+y)= f(x)f (v), Vx,y e R and lim f(x)=1. x0 Which of the following are necessarily true? (a) fis strictly increasing (b) fis either constant or bounded (c) S(rx)= S(x) for every rational r eQ ) f(x)20, VxeR