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Definition of Functions

Which of the ...

Question

Which of the following relations are functions from A = { 1, 4, 9, 16 } to B = { -1, 2, -3, -4, 5, 6 }. In case of a function, write down its range.
$f_{1}$ = { (1, -1), (4, 2), (9, -3), (16, -4) }

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Solution

Since every element of $A$ have a unique image in $B$ therefore $f_{1}$ is a function.

Range of $f_{1} =$ { $- 1, 2, - 3, - 4$ }

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Similar questions

Which of the following relations are functions from A = { 1, 4, 9, 16 } to B = { -1, 2, -3, -4, 5, 6 }. In case of a function, write down its range.

f_{2}

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

A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16}

f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

Are the following true?
(i)

f

is a relation from

A

B

f

is a function from

A

B

Justify your answer in each case

Q. Which of the following relations are functions? Give reasons.

If it is a function determine its domain and range
(i)

{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

{(1, 3), (1, 5), (2, 5)}

Q. 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)

R_{1}

={(x, y)| y=x+2, x

ϵ

ϵ

R_{2}

= { (1, 1), (2, 1), (3, 3), (4, 3), (5, 5) }
(iii)

R_{3}

= { (1, 1), (1, 3), (3, 5), (3, 7), (5, 7) }
(iv)

R_{4}

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

Q. 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}. Identify the type of function.

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