Let f : [0, ) [0,); f(x) = x b x 2 c Let g : Z Z; g(x) = 2x + 3

** Please only solve questions G-J**

CS2305 Homework 4 (Recall that Z -2,-1,0,1,2,...) is the integers, R the real numbers, (0, oo) the positive reals, and [0, oo) the non-negative reals.) Let f : [0, oo) [0.oo): f(z) x-L5 Let g : ZZ:g(x) = 2x + 3 a) What is the domain and codomain of f? b) What is the domain and codomain of g? c) Is f one-to-one? If not, show two elements of the domain which map to the same element of the codomain d) Is f onto? If not, show an element of the codomain which isn't mapped onto by any element of the domain e) Is g one-to-one? If not, show two elements of the domain which map to the same element of the codomain f) Is g onto? If not, show an element of the codomain which isn't mapped onto by any element of the domain g) Is the inverse function fdefined? If so, what is f(2) If not, why not? h) Is the inverse function g defined? If so, what is g(2)? If not, why not? i) Is the composition f o g defined? If so, what is (f o g)(2)? If not, why not? j) Is the composition g o f defined? If so, what is (go f) (2)? If not, why not