Answer to Question #129378 in Discrete Mathematics for jaya

Question

(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

Answer 1

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