Q13 of 99 Page 34

Show that the function f: N → Z, defined by


is both one - one and onto.



f(1) = 0


f(2) = - 1


f(3) = 1


f(4) = - 2


f(5) = 2


f(6) = - 3


Since at no different values of x we get same value of y ∴f(n) is one –one


And range of f(n) = Z = Z(codomain)


∴ the function f: N → Z, defined by



is both one - one and onto.


More from this chapter

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11

Show that the function f : R → R : f(x) = sin x is neither one - one nor onto.

 12

Prove that the function f : N → N : f(n) = (n2 + n + 1) is one - one but not onto.

 14

Find the domain and range of the function

F : R → R : f(x) = x2 + 1.


 15

Which of the following relations are functions? Give reasons. In case of a function, find its domain and range.

(i) f = {( - 1, 2), (1, 8), (2, 11), (3, 14)}


(ii) g = {(1, 1), (1, - 1), (4, 2), (9, 3),
(16, 4)}


(iii) h = {(a, b), (b, c), (c, b), (d, c)}