Question

Let A = {10, 11, 12, 13, 14}; B = {0, 1, 2, 3, 5} and f_i : A → B, i = 1, 2, 3. State the type of function for the following (give reason):

(i) f₁ = {(10,1), (11,2), (12,3), (13,5), (14,3)}

(ii) f₂ = {(10,1), (11,1), (12,1), (13,1), (14,1)}

(iii) f₃ = {(10,0), (11,1), (12,2), (13,3), (14,5)}

Answer 1

(i) The element 12 and 14 in A have same image 3 in B.

∴ It is not one-one function.

The element ‘0’ in B has no preimage in A.

∴ It is not onto function

So the given function is neither one – one nor onto function.

(ii) f₂ is a constant function

(iii) f₃ is one-one and onto function (or) bijective function.