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1. Relations and Functions
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Q6 of 107 Page 10

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.

It is given that A = {1, 2, 3}, B = {4, 5, 6, 7}

f: A → B is defined as f = {(1, 4), (2, 5), (3, 6)}


Therefore, f(1) = 4, f(2) = 5, f(3) = 6


We can see that the images of distinct elements of A under f are distinct.


Therefore, function f is one- one.


More from this chapter

All 107 →
4

Show that the Modulus Function f : R → R, given by f (x) = |x|, is neither one-one nor onto, where |x| is x, if x is positive or 0 and |x| is – x, if x is negative.

5

Show that the Signum Function f : R → R, given by


is neither one-one nor onto.

7

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

f : R → R defined by f (x) = 3 – 4x

7

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

f : R → R defined by f (x) = 1 + x2

Questions · 107
1. Relations and Functions
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