Today is our topic of discussion Function exercises 1.2 .
Function exercises 1.2
1. Which one is the domain of the relation {(2, 2), (4, 2), (2, 10), (7, 7)}?
1) {2,4,5,7}
3) {2,4,10,7}
2) {2, 2, 10, 7}
4) {2,4,7}
2. Given, S {(x, y) : x Є A, y Є A and y = x²} and A = {−2, -1,0,1,2} = which of the following is a member of the relation S?
1) (2,4)
3) (-1,1)
2) (-2,4)
4) (1,-1)
3. If S = {(1,4), (2, 1), (3, 0), (4, 1), (5, 4)} then,
(i) The range of the relation S is {4, 1,0}
(ii) The inverse relation of S is, S¹ = {(4, 1), (1, 2), (0, 3), (1, 4), (4, 5)}
(iii) The relation S is a function
Which combination of these statements is correct?
1) i and ii
2) ii and iii
3) i and iii
4) i, ii and iii
4. If F(x)=√x-1, then F(10) = ?
1) 9
2) 3
3) -3
4) √10
5. If S = {(x, y): x² + y² – 25 = 0 and x>0},
(i) The relation is not a function.
(ii) The graph of the relation is a half-circle.
(iii) The graph of the relation will be on upper half plane of the x axis.
Which one of the following is true?
1) i, ii
2) i, iii
3) ii, iii
6. If F(x)=√x-1=2, what is the value of x?
1) 5
2) 24
3) 25
4) 26
7. Which one below is the domain of the function F(x) = √x − 1?
1) Dom. F= {x R: x1}
2) Dom. F = {x Rx ≥1} 3) Dom. F= {x € R: x ≤ 1} 4) Dom. F= {ER: x > 1}
8.(i) Find the domain, range and inverse relation of the given relation S.
(ii) Ascertain whether relations S or S-¹ are functions.
(iii) Are the functions among these relations one-one?
1) S = {(1, 5), (2, 10), (3, 15), (4, 20)}
2) S={(-3,8), (-2, 3), (-1, 0), (0, -1), (1, 0), (2, 3), (3, 8)}
3) S= = {(1, 0), (1, 1), (1, −1) -1), (5, 2), (5, 2)}
4) S={(-3,-3), (-1, -1), (0, 0), (1, 1), (3, 3)}
5) S = {(2, 1), (2, 2), (2, 3)}
9. For the described function F(x) = = √x-1,
1) Find F(1), F(5) and F(10).
2) Find F(a² + 1) where a Є R.
3) If F(x)=5, find x.
4) If F(x)=y, find a where y ≥ 0.
10. For the function F: RR, F(x) = x³,
1) Find dom. F and range F.
3) Find F-1
2) Show that Fis a one-one function.
4) Show that F-1 is a function.
11. 1) If f: RR is a function which is defined by f(x) = ax + b; a, b = R, a0; show that ƒ is one-one and onto.
2) If ƒ [0, 1] → [0, 1] is a function which is defined by f(x) = √1 − x², show that ƒ is one-one and onto.
12. 1) If functions f: R→ R and g: R→ R are defined by f(x) = x³ +5 and g(x) = (x-5) then show that, g = ƒ˜¹.
2) If function f: R→ R is defined by f(x) = 5x-4, then, find y = ƒ-¹(x).
13. Draw the graph of the relation S and determine from the graph whether the relation is a function.
1) S = {(x, y): 2x − y + 5 = 0}
3) S= {(x, y): 3x + y = 4}
2) S = {(x, y): x + y = 1}
4) S = {(x, y): x = – -2}
14. Draw the graph of the relation S and determine (from the graph) whether the relation is function.
1) S = {(x, y): x² + y² = 25}
2) S = {(x, y): x²+y=9}
15. Given that, F(x) = 2x-1.
1) Find the values of F(x + 1) and F
2) Verify whether the function F(x) is one-one, when x, y Є R.
3) If F(x) = y, determine the values of y for three numerical values of and draw the graph of the equation y = 2x-1.
16. Two functions f: R→ R and g: R→ R are defined by f(x) = 3x + 3 and
g(x)= 3 respectively.
1) Find the value of g¹(-3).
2) Determine whether f(x) is an onto function.
3) Show that, g=f¹.
17. Given that, f(x) = √x −4.
1) Find the domain of f(x).
2) Determine whether f(x) is a one-one function.
3) Determine whether ƒ-1(x) is a function with the help of graph.
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