(b) Determine whether each of these function is a bijection (i) f : N → N such that f(n) = n 2 (ii) f : N → N such that f(n) = n + 3 1 (iii) f : R → R such that f(x) = x 3 (iv) f : R → R such that f(x) = x 2 + 1 (v) f : N → N such that f = ( n − 1 : n is odd n + 1 : n is even

1) y(n) = n2 is not bijective from its domain to N

{y element R : y>=0} (all non-negative real numbers)

2) y(n) = n + 3 is bijective from its domain to N. Range - all real numbers

3) y(x) = x3 is bijective from its domain to R. Range - all real numbers

4) y(x) = x2+1 is not bijective from its domain to R. {y element R : y>=1}

5) f is a bijection