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Maths-

General

Easy

Question

If A={1, 2, 3, 4}, then which of the following are functions from A to itself?

$f_{1} = {(x, y) ∣ y = x + 1}$
$f_{2} = {(x, y) ∣ x + y > 4}$
$f_{3} = {(x, y) ∣ y < x}$
$f_{4} = {(x, y) ∣ x + y = 5}$

The correct answer is: $f subscript 4 end subscript equals left curly bracket left parenthesis x comma y right parenthesis ∣ x plus y equals 5 right curly bracket$

We have $f subscript 1 end subscript equals left curly bracket left parenthesis 12 right parenthesis blank comma left parenthesis 23 right parenthesis blank comma left parenthesis 32 right parenthesis blank right curly bracket$
$f subscript 2 end subscript equals left curly bracket left parenthesis 12 right parenthesis blank comma left parenthesis 23 right parenthesis blank comma left parenthesis 22 right parenthesis blank comma left parenthesis 33 right parenthesis blank comma left parenthesis 44 right parenthesis blank comma left parenthesis 44 right parenthesis blank comma left parenthesis 42 right parenthesis blank comma left parenthesis 43 right parenthesis blank right curly bracket$
$f subscript 3 end subscript equals left curly bracket left parenthesis 21 right parenthesis blank comma left parenthesis 31 right parenthesis blank comma left parenthesis 32 right parenthesis blank horizontal ellipsis right curly bracket$
$f subscript 4 end subscript equals left curly bracket left parenthesis 14 right parenthesis blank comma left parenthesis 23 right parenthesis blank comma left parenthesis 32 right parenthesis blank comma left parenthesis 41 right parenthesis blank right curly bracket$
Obviously f₄ is a function from A to itself and $f subscript 1 end subscript comma f subscript 2 end subscript comma f subscript 3 end subscript$ are not functions from A to itself.

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