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RD Sharma Class 11 Maths Solutions Chapter Wise PDF
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RD Sharma Class 11 Maths Solutions Chapter 3 - Question with Solutions
1. Define a function.
Answer: A function is a relation where each element of set A (domain) has exactly one image in set B (codomain).
2. Is every relation a function? Explain.
Answer: No, because in a function, each input must have only one output.
3. Is the relation f(x) = x² a function?
Answer: Yes, because every x has only one square value.
4. If f(x) = 3x + 5, find f(2).
Answer: f(2) = 3×2 + 5 = 11.
5. Find the domain of f(x) = √(x − 3).
Answer: x ≥ 3, so Domain = [3, ∞)
6. Is f(x) = 1/x defined at x = 0?
Answer: No, it is undefined because division by zero is not allowed.
7. Give an example of a one-to-one function.
Answer: f(x) = 2x + 3 is one-to-one.
8. Give an example of a many-to-one function.
Answer: f(x) = x² because multiple inputs like 2 and -2 give the same output.
9. State the range of f(x) = |x|, x ∈ ℝ.
Answer: Range = [0, ∞).
10. If f(x) = x² + 1, find f(-2).
Answer: f(-2) = 4 + 1 = 5.
11. Find the domain of f(x) = 1/(x² − 4).
Answer: x ≠ ±2, so Domain = ℝ − {−2, 2}.
12. State whether f(x) = √(9 − x²) is defined for all x ∈ ℝ.
Answer: x ∈ [−3, 3].
13. Find f(3) if f(x) = 5x − 7.
Answer: f(3) = 15 − 7 = 8.
14. Find the range of f(x) = 2x + 5, x ∈ [1, 3].
Answer: Range = [7, 11].
15. If f(x) = sin x, what is its domain and range?
Answer: Domain = ℝ, Range = [−1, 1].
16. Is f(x) = constant (say 7) a function?
Answer: Yes, every input gives the same output 7.
17. Give an example of an identity function.
Answer: f(x) = x.
18. Define even and odd functions.
Answer: Even: f(-x) = f(x); Odd: f(-x) = −f(x).
19. Find the domain of f(x) = log(x + 2).
Answer: Domain = (−2, ∞).
20. Is f(x) = tan x defined at x = 90°?
Answer: No, tan 90° is undefined.
21. Give an example of a periodic function.
Answer: f(x) = sin x, period = 2π.
22. State whether f(x) = eˣ is increasing or decreasing.
Answer: Increasing function.
23. Is f(x) = |x| an even function?
Answer: Yes, because f(-x) = f(x).
24. Find f(-1) when f(x) = x³ + 2x² − x + 4.
Answer: f(-1) = 6.
25. What is the domain of f(x) = √(1 − x²)?
Answer: Domain = [−1, 1].
Frequently Asked Questions
A function is a special type of relation where each element of the domain (input set) is connected to exactly one element of the codomain (output set). It means every input has one and only one output
In a relation, an element of the domain can have multiple outputs. But in a function, every element of the domain has only one unique output.
The common types of functions in this chapter include:
- One-to-one (Injective) function
- Many-to-one function
- Onto (Surjective) function
- Into function
- Constant function
- Identity function
Domain is the set of all possible input values of a function.
Range is the set of all possible output values the function can produce.
An identity function is a function where the output is always the same as the input. It is written as f(x) = x.
A constant function is a function where every input has the same constant output. For example, f(x) = 5 means all inputs give the output 5.
Yes, f(x) = x² is a function because every value of x gives only one squared value.