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)}


For a relation to be a function each element of 1st set should have different image in the second set(Range)


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


Here, each of the first set element has different image in second set.


∴f is a function whose domain = { - 1, 1, 2, 3} and range (f) = {2, 8, 11, 14}


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


Here, some of the first set element has same image in second set.


∴ g is not a function.


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


Here, each of the first set element has different image in second set.


∴h is a function whose domain = {a, b, c, d} and range (h) = {b, c}


(range is the intersection set of the elements of the second set elements.)


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