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, 2, 3, 4,...} , {1,2,3,4}, {2, 4, 6, 8,...} , yes.
yes
(i) 12 (ii) $4a^2 - 10a + 6$ (iii) 0 (iv) $x^2 - 7x + 12$
(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
2
(i) -2 (ii) 3/2 (iii) 3 (iv) 1/2
$4x^3 - 96x^2 + 576x$
1
500t
(i) Yes (ii) 0.9, 24.5 (iii) 60.5 inches (iv) 32 cms