Q6 of 50 Page 28

A = {–2, –1, 1, 2 } and . Write down the range of f. Is f a function from A to A?

From the elements of A we can write the function in set order


So f =


Here from the above expression the range of the function is given as


Range of f =


As the element of the range are not in the set A so clearly it’s not a function from A to A.


More from this chapter

All 50 →
4

If X = {1, 2, 3, 4, 5 }, Y = { 1, 3, 5, 7, 9 } determine which of the following relations from X to Y are functions? Give reason for your answer. If it is a function, state its type.

(i) R1 = {(x, y)| y = x + 2, x ∈ X , y ∈ Y }


(ii) R2 = {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)}


(iii) R3 = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}


(iv) R4 = {(1, 3), (2, 5), (4, 7), (5, 9), (3, 1)}

 5

If R = {(a, - 2), (- 5, b), (8, c), (d, - 1)} represents the identity function, find the values of a, b, c and d.

 7

Let f = {(2, 7), (3, 4), (7, 9), (–1, 6), (0, 2), (5, 3) } be a function from A = { –1, 0, 2, 3, 5, 7 } to B = { 2, 3, 4, 6, 7, 9}.

 8

Write the pre-images of 2 and 3 in the function

f = { (12, 2), (13, 3), (15, 3), (14, 2), (17, 17) }.