10th Maths Book Back Question & Answers – Chapter 1 Exercise 1.3:
Samacheer Kalvi 10th Standard Maths Book Back Questions with Answers PDF uploaded and the same given below. Class-tenth candidates and those preparing for TNPSC exams can check the Maths Book Back Answers PDF below. Samacheer Kalvi Class 10th Std Maths Book Back Answers Chapter 1 Exercise 1.3 Solutions are available below. Check the complete Samacheer Kalvi 10th Maths – Relations and Functions Ex 1.3 Book Back Answers below:
We also provide class 10th other units Maths Book Back One and Two Mark Solutions Guide on our site. Students looking for the 10th standard Maths Ex 1.3 – Relations and Functions Book Back Questions with Answer PDF
For the complete Samacheer Kalvi 10th Maths Book Back Solutions Guide PDF, check the link – Samacheer Kalvi 10th Maths Book Back Answers
Samacheer Kalvi 10th Maths Book Back Answers – Ex 1.3 Relations and Functions
Samacheer Kalvi 10th Maths Book Subject One Mark, Two Mark, Five Mark Guide questions and answers are below. Check Maths Book Back Questions with Answers. Take the printout and use it for exam purposes.
For Samacheer Kalvi 10th Maths Book PDF, check the link – 10th Maths Book PDF
Chapter 3
Exercise 1.3 Relations and Functions
1. Let f = {(x, y)|x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain, and range. Is this relation a function?
Solution:
F = {(x, y)|x, y ∈ N and y = 2x}
x = {1, 2, 3,…}
y = {1 × 2, 2 × 2, 3 × 2, 4 × 2, 5 × 2 …}
R = {(1, 2), (2, 4), (3, 6), (4, 8), (5, 10),…}
Domain of R = {1, 2, 3, 4,…},
Co-domain = {1, 2, 3…..}
Range of R = {2, 4, 6, 8, 10,…}
Yes, this relation is a function.
2. Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x))|x ∈ X, f(x) = x2 + 1} is a function from X to N?
Solu.:
x = {3,4, 6, 8}
R = ((x, f(x))|x ∈ X, f(x) = X2 + 1}
f(x) = x2 + 1
f(3) = 32 + 1 = 10
f(4) = 42 + 1 = 17
f(6) = 62 + 1 = 37
f(8) = 82 + 1 = 65
R = {(3, 10), (4, 17), (6, 37), (8, 65)}
R = {(3, 10), (4, 17), (6, 37), (8, 65)}
Yes, R is a function from X to N.
3. Given the function
f : x → x2 – 5x + 6, evaluate
(i) f(-1)
(ii) f(2 a)
(iii) f(2)
(iv) f(x – 1)
Solu.:
f(x) = x2 – 5x + 6
(i) f (-1) = (-1)2 – 5 (-1) + 6 = 1 + 5 + 6 = 12
(ii) f (2a) = (2a)2 – 5 (2a) + 6 = 4a2 – 10a + 6
(iii) f(2) = 22 – 5(2) + 6 = 4 – 10 + 6 = 0
(iv) f(x – 1) = (x – 1)2 – 5 (x – 1) + 6
= x2 – 2x + 1 – 5x + 5 + 6
= x2 – 7x + 12
4. A graph representing the function f(x) is given in figure 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?
Solu.:
From the graph
(a) f(0) = 9
(b) f(7) = 6
(c) f(2) = 6
(d) f(10) = 0
(ii) At x = 9.5, f(x) = 1
(iii) Domain = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
= {x |0 < x < 10, x ∈ R}
Range = {x|0 < x < 9, x ∈ R}
= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
(iv) The image of 6 under f is 5.
5. Let f(x) = 2x + 5. If x ≠ 0 then find f(x+2)−f(2)x
Solu.:
Given f(x) = 2x + 5, x ≠ 0.
6. A function fis defined by f(x) = 2x – 3
(i) find 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).
Solu.:
Given f(x) = 2x – 3
(i) find f(0)+f(1)2
f(0) = 2(0) – 3 = -3
f(1) = 2(1) – 3 = -1
∴ f(0)+f(1)2=−3−12=−42 = -2
(ii) f(x) = 0
⇒ 2x – 3 = 0
2x = 3
x = 32
(iii) f(x) = x
⇒ 2x – 3 = x ⇒ 2x – x = 3
x = 3
(iv) f(x) = f(1 – x)
2x – 3 = 2(1 – x) – 3
2x – 3 = 2x – 2x – 3
2x + 2x = 2 – 3 + 3
4x = 2
x = 24
x = 12
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 in the figure. Express the volume V of the box as a function of x.
Solu.:
Volume of the box = Volume of the cuboid
= l × b × h cu. units
Here l = 24 – 2x
b = 24 – 2x
h = x
∴ V = (24 – 2x) (24 – 2x) × x
= (576 – 48x – 48x + 4x2)x
V = 4x3 – 96x2 + 576x
8.A function f is defined bv f(x) = 3 – 2x . Find x such that f(x2) = (f(x))2.
Solution:
f(x) = 3 – 2x
f(x2) = 3 – 2x2
9. A plane is flying at a speed of 500 km per hour. Express the distance traveled by plane as a function of time r in hours.
Solu.:
Speed of the plane = 500 km/hr
Distance traveled in “t” hours
= 500 × t (distance = speed × time)
= 500 t
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 the forehand of a woman if her height is 53.3 inches.
Solu.:
(i) Given y = ax + b …………. (1)
The ordered pairs are R = {(35, 56) (45, 65) (50, 69.5) (55, 74)}
∴ Hence this relation is a function.
Substituting a = 0.9 in (2) we get
⇒ 65 = 45(.9) + b
⇒ 65 = 40.5 + b
⇒ b = 65 – 40.5
⇒ b = 24.5
∴ a = 0.9, b = 24.5
∴ y = 0.9x + 24.5
(iii) Given x = 40 , y = ?
∴ (4) → y = 0.9 (40) + 24.5
⇒ y = 36 + 24.5
⇒ y = 60.5 inches
(iv) Given y = 53.3 inches, x = ?
(4) → 53.3 = 0.9x + 24.5
⇒ 53.3 – 24.5 = 0.9x
⇒ 28.8 = 0.9x
⇒ x = 28.80.9 = 32 cm
∴ When y = 53.3 inches, x = 32 cm
Other Important Links for 10th Maths Book Back Answers Solutions:
For 10th Maths, chapter 1 book back question and answers, check the link – Samacheer Kalvi 10th Maths Chapter 1 Relations and Functions
Click here for the complete Samacheer Kalvi 10th Book Back Solution Guide PDF – 10th Maths Book Back Answers