Class 11 Maths Chapter 2 Relations and Functions – Exercise 2.3 NCERT Solutions

Introduction

Exercise 2.3 introduces the concept of functions as special types of relations. A function maps each element of the domain to exactly one element of the codomain. You will learn how to identify functions, determine their domain and range, and classify them as one‑one or onto.

Key Definitions

1. Function: A relation $f:A\to B$ is a function if every element of $A$ is related to exactly one element of $B$.

2. Domain: Set of all first elements of ordered pairs.

3. Range: Set of all second elements actually mapped.

4. Codomain: The target set $B$.

5. One‑One Function (Injective): Different elements of domain map to different elements of codomain.

6. Onto Function (Surjective): Every element of codomain has a pre‑image in domain.

NCERT Questions with Solutions (10)

Q1. Check if relation $f:A\to B$ defined by $f(x)=x^2$, $A=\{1,2,3\},B=\{1,4,9\}$ is a function. Yes, each $x\in A$ maps to exactly one element in $B$.

Q2. Check if relation $f:A\to B$ defined by $f(x)=\pm x$ is a function. No, since each $x$ maps to two values ($+x$ and $-x$).

Q3. If $f:A\to B$ defined by $f(x)=2x$, $A=\{1,2,3\},B=\{2,4,6\}$, find domain and range. Domain = $\{1,2,3\}$, Range = $\{2,4,6\}$.

Q4. If $f:A\to B$ defined by $f(x)=x+1$, $A=\{1,2,3\},B=\{2,3,4\}$, check if function is one‑one. Yes, distinct inputs give distinct outputs.

Q5. If $f:A\to B$ defined by $f(x)=x^2$, $A=\{-1,0,1\},B=\{0,1\}$, check if function is one‑one. No, since $f(-1)=f(1)=1$.

Q6. If $f:A\to B$ defined by $f(x)=x^2$, $A=\{1,2,3\},B=\{1,4,9\}$, check if function is onto. Yes, every element of $B$ has a pre‑image in $A$.

Q7. If $f:A\to B$ defined by $f(x)=x+2$, $A=\{1,2,3\},B=\{3,4,5\}$, check if function is onto. Yes, each element of $B$ is covered.

Q8. If $f:A\to B$ defined by $f(x)=x^2$, $A=\{1,2,3\},B=\{1,4,9,16\}$, check if function is onto. No, since 16 has no pre‑image in $A$.

Q9. If $f:A\to B$ defined by $f(x)=x$, $A=\{1,2,3\},B=\{1,2,3\}$, check if function is one‑one and onto. Yes, it is both one‑one and onto (bijective).

Q10. If $f:A\to B$ defined by $f(x)=x^2$, $A=\{-2,-1,0,1,2\},B=\{0,1,4\}$, check if function is one‑one. No, since $f(-2)=f(2)=4$.

FAQs (10)

1. What is a function? A relation where each input has exactly one output.

2. What is domain? Set of inputs.

3. What is range? Set of outputs actually obtained.

4. What is codomain? Target set of outputs.

5. What is one‑one function? Distinct inputs give distinct outputs.

6. What is onto function? Every element of codomain is mapped.

7. What is bijective function? Function that is both one‑one and onto.

8. Can a function map one input to two outputs? No.

9. Can two inputs map to same output? Yes, but then function is not one‑one.

10. Why is this exercise important? It builds foundation for advanced function concepts in Class 11 and 12.

Conclusion

Exercise 2.3 has 10 solved questions and 10 FAQs that strengthen your understanding of functions, domain, range, and types of mappings. This builds the foundation for advanced function theory in Class 11 Maths.

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