Which of the following relations are functions? Give reasons. In case

1.	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)}
Answer» For a relation to be a function each element of 1^st 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.)

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)}

Answer»

For a relation to be a function each element of 1^st 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.)