10th Maths Exercise 1.3: Functions | Problems, Answers & Solutions

Exercise 1.3: Functions - Problem Questions with Answer, Solution

Maths Book back answers and solution for Exercise questions - Mathematics : Function: Exercise Questions with Answer

Question 1

Let $f = \{(x,y) | x,y \in \mathbf{N} \text{ and } y = 2x\}$ be a relation on N. Find the domain, co-domain and range. Is this relation a function?

Question 2

Let $X = \{3, 4, 6, 8\}$. Determine whether the relation $R = \{(x, f(x)) | x \in X, f(x) = x^2 + 1\}$ is a function from $X$ to $\mathbf{N}$?

Question 3

Given the function $f : x \to x^2 - 5x + 6$, evaluate

• (i) $f(-1)$
• (ii) $f(2a)$
• (iii) $f(2)$
• (iv) $f(x-1)$

Question 4

A graph representing the function $f(x)$ is given in Fig.1.16 it is clear that $f(9) = 2$.

(i) Find the following values of the function

• (a) $f(0)$
• (b) $f(7)$
• (c) $f(2)$
• (d) $f(10)$

(ii) For what value of $x$ is $f(x) = 1$?

(iii) Describe the following (i) Domain (ii) Range

(iv) What is the image of 6 under $f$?

Question 5

Let $f(x) = 2x+5$. If $x \neq 0$ then find

$\frac{f(x+2) - f(2)}{x}$

Question 6

A function $f$ is defined by $f(x) = 2x - 3$

• (i) find $\frac{f(0) + f(1)}{2}$
• (ii) find $x$ such that $f(x) = 0$
• (iii) find $x$ such that $f(x) = x$
• (iv) find $x$ such that $f(x) = f(1 - x)$

Question 7

An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown (Fig.1.17). Express the volume $V$ of the box as a function of $x$.

Question 8

A function $f$ is defined by $f(x) = 3 - 2x$. Find $x$ such that $f(x^2) = (f(x))^2$.

Question 9

A plane is flying at a speed of 500 km per hour. Express the distance $d$ travelled by the plane as function of time $t$ in hours.

Question 10

The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height. Based on this data, a student finds a relationship between the height ($y$) and the forehand length($x$) as $y = ax + b$, where $a, b$ are constants.

• (i) Check if this relation is a function.
• (ii) Find $a$ and $b$.
• (iii) Find the height of a woman whose forehand length is 40 cm.
• (iv) Find the length of forehand of a woman if her height is 53.3 inches.

Quick Answers

1. {1, 2, 3, 4,...} , {1,2,3,4}, {2, 4, 6, 8,...} , yes.
2. yes
3. (i) 12 (ii) $4a^2 - 10a + 6$ (iii) 0 (iv) $x^2 - 7x + 12$
4. (i) (a) 9 (b) 6 (c) 6 (d) 0 (ii) 9.5 (iii) (a) $\{x | 0 \le x \le 10, x \in R\}$ (b) $\{x | 0 \le x \le 9, x \in R\}$ (iv) 5
5. 2
6. (i) -2 (ii) 3/2 (iii) 3 (iv) 1/2
7. $4x^3 - 96x^2 + 576x$
8. 1
9. 500t
10. (i) Yes (ii) 0.9, 24.5 (iii) 60.5 inches (iv) 32 cms

10th Maths Unit 1: Relations and Functions Exercise 1.1 Solutions | Cartesian Product

Exercise 1.1: Cartesian Product - Solutions

Maths Book back answers and solution for Exercise questions - Mathematics : Relation and Function: Cartesian Product: Exercise Questions with Answer, Solution

Question 1

Find \(A \times B\) , \(A \times A\) and \(B \times A\)

(i) \(A = \{2, -2, 3\}\) and \(B = \{1, -4\}\)

(ii) \(A = B = \{p, q\}\)

(iii) \(A = \{m, n\}\) ; \(B = \emptyset\)

Solution:

Question 2

Let \(A = \{1,2,3\}\) and \(B = \{x | x\) is a prime number less than 10}. Find \(A \times B\) and \(B \times A\).

Solution:

Question 3

If \(B \times A = \{(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)\}\) find A and B.

Solution:

Question 4

If \(A = \{5, 6\}\) , \(B = \{4, 5, 6\}\) , \(C = \{5, 6, 7\}\) , Show that \(A \times A = (B \times B) \cap (C \times C)\) .

Solution:

Question 5

Given A={1,2,3}, \(B = \{2,3,5\}\), \(C = \{3,4\}\) and \(D = \{1,3,5\}\), check if \((A \cap C) \times (B \cap D) = (A \times B) \cap (C \times D)\) is true?

Solution:

Question 6

Let \(A = \{x \in W | x < 2\}\) , \(B = \{x \in N | 1 < x \le 4\}\) and \(C = \{3, 5\}\). Verify that

(i) \(A \times (B \cup C) = (A \times B) \cup (A \times C)\)

(ii) \(A \times (B \cap C) = (A \times B) \cap (A \times C)\)

(iii) \((A \cup B) \times C = (A \times C) \cup (B \times C)\)

Solution:

Question 7

Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that

(i) \((A \cap B) \times C = (A \times C) \cap (B \times C)\)

(ii) \(A \times (B - C) = (A \times B) - (A \times C)\)

Solution:

Final Answers

• 1. (i) \(A \times B = \{(2, 1), (2, -4), (-2, 1), (-2, -4), (3, 1), (3, -4)\}\)
  \(A \times A = \{(2, 2), (2, -2), (2, 3), (-2, 2), (-2, -2), (-2, 3), (3, 2), (3, -2), (3, 3)\}\)
  \(B \times A = \{(1, 2), (1, -2), (1, 3), (-4, 2), (-4, -2), (-4, 3)\}\)
• 1. (ii) \(A \times B = \{(p, p), (p, q), (q, p), (q, q)\}\)
  \(A \times A = \{(p, p), (p, q), (q, p), (q, q)\}\)
  \(B \times A = \{(p, p), (p, q), (q, p), (q, q)\}\)
• 1. (iii) \(A \times B = \{\}\)
  \(A \times A = \{(m, m), (m, n), (n, m), (n, n)\}\)
  \(B \times A = \{\}\)
• 2. \(A \times B = \{(1, 2), (1, 3), (1, 5), (1, 7), (2, 2), (2, 3), (2, 5), (2, 7), (3, 2), (3, 3), (3, 5), (3, 7)\}\)
  \(B \times A = \{(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (5, 1), (5, 2), (5, 3), (7, 1), (7, 2), (7, 3)\}\)
• 3. \(A = \{3, 4\}\) and \(B = \{-2, 0, 3\}\)
• 5. True