The document contains definitions of relations and functions through sets of ordered pairs. It includes relations defined by properties or equations, and functions defined as sets of inputs and outputs. It poses problems involving evaluating functions at given inputs, finding compositions of functions, and performing arithmetic operations on functions.

1. 31202
2 ………..
–
4/……………………..

2. A B A
B
4
0
1

3. 1 {1, 2} {3, 4, 5} {(1, 3), (1, 4), (1, 5), (2, 3),
(2, 4), (2, 5)}
2 {a} {1, 2} {(a, 1), (a, 2)}
3 {3, 4} {a, b, c}
4 {2, 4} {5, 6}
5 {a, b} {3, 4, 5,
6}
6 {1, 2, 3} {5, 7, 9}
7 {a, b, c} {2, 4}
8 {x, y} {1, 2, 3}
9 {1, 2} {1, 2}
10 {m, n} {x, y}

4. 1.
2. (10, 6)
3. (2, 3) ( 4 , 3)
4.
4.1
4.1 (x, y) = (6, 9)
……………………
4.2 (x – 2, 4) = (8, y + 2)
…….
4.3 (-3, a) = (b – 4, 6)
4.2
4.4 (x + y, x – y) = (6, 4)
……………………
4.5 (2x, y) = (16, 2)
…….
4.3
……………………
…….
4.4
……………………
…….
4.5
……………………

5. …….
1. A = {3} B = {5, 6}
1.1 A B =
………………………………………………………………….
1.2 B A =
………………………………………………………………….
1.3 A A =
………………………………………………………………….
1.4 B B =
………………………………………………………………….
2. A = {1, 3} B = {5, 7, 9}
2.1 A B =
………………………………………………………………….
2.2 B A =
………………………………………………………………….
2.3 A A =
………………………………………………………………….
2.4 B B =
………………………………………………………………….

6. 3. A = {2, 4} B = {6, 8, 10, 12}
3.1 A B
=……………………………………………
3.2 B B
=……………………………………………
2
1. r = {(2, 4), (3, 7), (1, 5)}
2. r = {(0, 0), (-1, -1), (-2, -2), (-3, -3), (-4, -
4)}

7. 3. r = {(x, y) I I | x2 + y2 = 4}
x
y
4. r = {(x, y) I I | y = x + 3}
x

8. y
4. r = {(x, y) | 2 x 5}
5. r = {(x, y) | y = x2 - 2 }
x
y

9. 3
1. r = {(1, 2), (2, 4), (3, 5), (4, 6)}
1.1 Dr =
………………………………………………………………
…
1.2 Rr =
………………………………………………………………
…
2. r = {(-2, 5), (3, 7), (6, 6), (6, 2), (4, 8)}
2.1 Dr =

10. 1 {(1, a), (2, b), (3, c), (4,

11. d)}
2 {(2, 10), (3, 20), (4, 30),
(5, 40)}
3 {(1, 3), (2, 4), (3, 5), (4,
6)}
4 {(0, 0), (1, 1), (2, 2), (3,
3)}
5 {(1, 4), (2, 5), (3, 6), (4,
7)}
6 {(1, 1), (2, 4), (3, 9), (4,
16)}
7 {(0, 0), (1, 2), (2, 4), (3,
6), (4, 8)}
8 {(x, y) | y = x - 4}
9 {(x, y) I I | y = x2 +
1}
10 {(x, y) | y = x-8}
r
r-1 r-1
1 {(1, a), (2, b), (3, c),
(4, d)}

12. 2 {(2, 10), (3, 20), (4,
30), (5, 40)}
3 {(1, 3), (2, 4), (3, 5),
(4, 6)}
4 {(0, 0), (1, 1), (2, 2),
(3, 3)}
5 {(1, 4), (2, 5), (3, 6),
(4, 7)}
6 {(1, 1), (2, 4), (3, 9),
(4, 16)}
7 {(0, 0), (1, 2), (2, 4),
(3, 6), (4, 8)}
8 {(x, y) | y = x - 4}
9 {(x, y) I I | y =
x2 + 1}
1 {(x, y) | y = x-8}
0
1 {(x, y) | y = }
1
1 {(x, y) | y = 3x+ 2}
2
4

13. 
1 r = {(1, 2), (3, 7), (4, 9), (8,
6), (10, 8)}
2 r = {(3, 2), (4, 2), (6, 2)}
3 r = {(1, 3), (2, 4), (3, 6), (3,
8)}
4 r = {(x, y) | y = x2 - 1}
5 r = {(x, y) | xy = 2}
6 r = {(x, y) | y2 = x + 3}
7 r = {(x, y) | y = x3}
8 r = {(x, y) | y = x2 + 3}
9 r = {(2, 3), (2, 4), (3, 6), (4,
9)}
10 r = {(x, y) | x = y2 + 2y + 1}
1 r1 = {(3, 2), (-1, 4), (0, 2), (5, -
3)}

14. 2 r2 = {(1, -1), (-1, -1), (0, 1), (3,
1)}
3 r3 = {(4, 2), (4, 3), (5, 4), (6,
6)}
4 r4 = {(6, 1), (6, 1), (7, 2), (8,
3), (9, 4)}
5 r5 = {(2, 1), (2, 3), (3, 4), (4,
5), (5, 6)}
6 r6 = {(x, y) | y = 3x – 1}
7 r7 = {(x, y) | y = 3x2– x + 3}
8 r8 = {(x, y) | y = 2x2 + 1}
9 r9 = {(x, y) | y = 4x2}
10 r10 = {(x, y) | x2 + y2 = 4 , x
0}
f = {(1, 2), (2, 4), . Y
(3, 6), (4, 8)}
1-3
0 X
1. f
. y = 2x
Y . Y
. y = 3x
. y = 2x + 1 1
. y 0= x + 1 X x 2 4 6 08
f(x 1 2 3 4
Y
x 0 2 3 4
)
f(x 2 4 6 8
x 2 4 6 4
)

15. 2. fX
3. f
.
.
.
.
.
.
1 f = {(2, 5), (3, 7), (4, 9), {2, 3, 4, {5, 7, 9,
(5, 11)} 5} 11}
2 f = {(a, 1), (b, 2), (c, 3),
(d, 4)}
3 f = {(m, 2), (n, 4), (p, 6)}
4 f = {(4, 7), (6, 9), (8, 11)}
5 f = {(2, 1), (3, 2), (4, 3),
(5, 4)}
6 f = {(a, 10), (b, 10), (c,
10)}

16. 7 f = {(3, 6), (5, 10), (7, 14)}
8 f = {(1, 4), (2, 5), (3, 6),
(4, 7)}
5
1. f(x) = 2x2 – x + 5 g(x) = x + 1
1.1 (f + g )(x)
1.2 (f – g)(-2)
1.3 (fg)(3)
1.4 ( )(0)
…………………………………………………………………………
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17. …………………………………………………………………………
…………………………………………………………………………
…………………………………………………………………………
2. f(x) = 3x – 5 g(x) =
2.1 (f + g) (-3)
2.2 (fg)(6)
…………………………………………………………………………
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3. f(x) = 2x + 10 g(x) =
3.1 (f + g)(x)
3.2 (fg)(2)
3.3 (f-g)(3)

18. 3.4 ( )(x)
…………………………………………………………………………
…………………………………………………………………………
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19. …………………………………………………………………………
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6
1. f(x) = 3x – 5 g(x) = 1 – x2
1.1 f(g(0)) =…………………………........ 1.2 g(f(0))
=………………………………….

20. =……………………………….
=………………………………….
=……………………………….
=………………………………….
=……………………………….
=………………………………….
1.3 f(f(4)) =…………………………........ 1.4 g(g(1))
=…………………………………
=……………………………….
=………………………………….
=……………………………….
=………………………………….
=……………………………….
=………………………………….
1.5 (f g)(-2) =…………………………........ 1.6 (g f)(-2)
=………………………………
=……………………………….
=………………………………….
=……………………………….
=………………………………….
=……………………………….
=………………………………….
1.7 (f f)(-1) =…………………………........ 1.8 (g g)(2)
=………………………………

21. =……………………………….
=………………………………….
=……………………………….
=………………………………….
=……………………………….
=………………………………….
1.9 (f g)(x) =…………………………........ 1.10
(g f)(x) =……………………………
=……………………………….
=………………………………….
=……………………………….
=………………………………….
=……………………………….
=………………………………….
1.11 (f f)(x) =…………………………........ 1.12
(g g)(x) =………………………………
=……………………………….
=………………………………….
=……………………………….
=………………………………….
=……………………………….
=………………………………….
2. f g, g f,f f g g

22. 2.1 f(x) = 3x + 2 , g(x) = 4x -1 2.2 f(x) = 5x – 6
, g(x) =
f g =………………………………………. f g
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g f =………………………………………. g f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

23. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f f =………………………………………. f f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g g =………………………………………. g g
=……………………………………….
=……………………………………….
=……………………………………….

24. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
2.3 f(x) = x2 , g(x) = x + 5 2.4 f(x) = x3 + 1
, g(x) = x + 2
f g =………………………………………. f g
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

25. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g f =………………………………………. g f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f f =………………………………………. f f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

26. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g g =………………………………………. g g
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

27. 2.5 f(x) = , g(x) = 2x + 3 2.6 f(x) = x2 ,
g(x) =
f g =………………………………………. f g
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g f =………………………………………. g f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

28. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f f =………………………………………. f f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g g =………………………………………. g g
=……………………………………….
=……………………………………….
=……………………………………….

29. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
2.7 f(x) = x , g(x) = 2x + 5 2.8 f(x) = x + 4
, g(x) = x–4
f g =………………………………………. f g
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

30. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g f =………………………………………. g f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f f =………………………………………. f f
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

31. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
g g =………………………………………. g g
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
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32. 7
1. f
1.1 f(3) = 10 f-1 (10) =
………………………………………
1.2 f-1(3) = -4 f- (-4) =
………………………………………
1.3 f(10) = 18 f-1 (18) =
………………………………………
1.4 f-1(4) = 3 f- (3) =
…………………………………………
1.5 f(x) = 5 + 2x f-1 (10) =
………………………………………
1.6 f(x) = x2 + 4x x ≥ -2 f-1 (112) =
…………………………………….
2. f
2.1 f(x) = 3x + 1 2.2 f(x) = 5 - x
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

33. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f-1(x) =…………………………………….
f-1(x) =……………………………
2.3 f(x) = 5x + 7 2.4 f(x) = 5 - 3x
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
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=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f-1(x) =…………………………………….
f-1(x) =……………………………
2.5 f(x) = 2.6 f(x) = , x >
0
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

34. =……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f-1(x) =…………………………………….
f-1(x) =……………………………
2.7 f(x) = 2.8 f(x) = 3 – 4x5
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
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=……………………………………….
=……………………………………….
=……………………………………….
f-1(x) =…………………………………….
f-1(x) =……………………………
2.9 f(x) = 2.10 f(x) = x2 + x , x
≥ -

35. =……………………………………….
=……………………………………….
=……………………………………….
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=……………………………………….
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=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f-1(x) =…………………………………….
f-1(x) =……………………………
2.11 f(x) = 5 – x2 , x ≥ 0 2.12 f(x) = (4 –
x3)5
=……………………………………….
=……………………………………….
=……………………………………….
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=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….

36. f-1(x) =…………………………………….
f-1(x) =……………………………
2.13 f(x) = x6 2.14 f(x) = 3 – x3
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
=……………………………………….
f-1(x) =…………………………………….
f-1(x) =……………………………