f(3) for f(x) = 2x + 1 comes out as 7, and the domain of f(x) = √x is x ≥ 0, so this Class 11 sheet opens by evaluating a function and fixing its square-root domain. The answers record 15 for a later value and A × B for a Cartesian product.
Key Takeaways
f(3) = 7 when f(x) = 2x + 1 (Q1).
The domain of f(x) = √x is x ≥ 0 (Q2).
Q4 records A × B as a Cartesian product.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.If f(x) = 2x + 1, then f(3) = ?
(a) 6(b) 7(c) 5(d) 8
2.The domain of the real valued function f(x) = √x is:
(a) All real numbers(b) x ≥ 0(c) x > 0(d) x ≠ 0
3.If f(x) = x² and g(x) = 2x, then (f + g)(3) = ?
(a) 9(b) 15(c) 13(d) 6
4.A relation R from set A to set B is a subset of:
(a) A ∪ B(b) A × B(c) A ∩ B(d) B - A
5.If A = {1, 2} and B = {3, 4}, then the number of elements in A × B is:
(a) 2(b) 4(c) 6(d) 8
6.If f(x) = x³ - x, then f(-1) = ?
(a) 0(b) -2(c) -1(d) 2
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Define a function from a set A to a set B.
8.Find the domain of the real valued function f(x) = 1/(x - 2).
9.If f(x) = 3x - 5, find f(2) + f(-1).
10.If A = {1, 2} and B = {3, 4}, write the cartesian product A × B.
11.State the range of the function f(x) = x² for x ∈ R.
12.If f(x) = x + 1/x, find f(2).
13.If A = {1, 2, 3} and B = {4, 5, 6}, define the relation R = {(x, y) : y = x + 3} and write it in roster form.
14.What is the range of the identity function f(x) = x on R?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The taxi fare in a city is ₹8 for the first kilometre and ₹5 for each further kilometre. If f(x) is the fare for x kilometres, write f(x) for x ≥ 1 and find the fare for 6 kilometres.
16.A function f is defined by f(x) = 2x - 1. If the domain is the set {0, 1, 2, 3}, find the range of f.
17.If f(x) = x² - 4x + 3, find the values of x for which f(x) = 0.
18.A manufacturer sells each unit at ₹120. The fixed cost is ₹2000 and the variable cost is ₹40 per unit. Express the profit P(x) for selling x units and find the profit for 50 units.
19.The monthly salary of a salesperson is ₹15000 plus 5% commission on total sales. If the sales in a month are ₹60000, find the total earnings for that month.
20.If f(x) = x³, find the value of f(2) - f(1).
Answer Key
1. b) 7
2. b) x ≥ 0
3. b) 15
4. b) A × B
5. b) 4
6. a) 0
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is f(3) when f(x) = 2x + 1?
7, option (b) in this worksheet (Q1).
What is the domain of f(x) = √x?
x ≥ 0, option (b) in this worksheet (Q2).
What is the set of ordered pairs from A to B?
A × B, option (b) in this worksheet (Q4).
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