# Tamilnadu State board 10th Maths Answers Chapter 1 Relations and Functions Exercise 1.3 ( EX 1.3 )

## You can Download and practice Tamilnadu state board 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Reduced Syllabus and score more marks in your Public examinations and assignment writing work

# Tamilnadu State board 10th Maths Solutions Chapter 1 Relations and Functions Exercise 1.3 ( EX 1.3 )

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?

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.

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 ?

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.

Given the function

f : x → x2 – 5x + 6, evaluate

(i) f(-1)

(ii) f(2 a)

(iii) f(2)

(iv) f(x – 1)

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

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?

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.

Let f(x) = 2x + 5. If x ≠ 0 then

find `frac{f(x+2)-f(2)}{x}`

Solution:

Given f(x) = 2x + 5, x ≠ 0

- $\frac{\mathrm{Question\; 6.}}{}$

A function fis defined by f(x) = 2x – 3

(i) find `frac{f(0)+f(1)}{2}`

$\frac{\mathrm{(ii)\; find\; x\; such\; that\; f(x)\; =\; 0.(iii)\; find\; x\; such\; that\; f(x)\; =\; x.(iv)\; find\; x\; such\; that\; f(x)\; =\; f(1\; \u2013\; x).Solution:Given\; f(x)\; =\; 2x\; \u2013\; 3(i)\; find\; `frac\{f(0)+f(1)\}\{2\}`f(0)\; =\; 2(0)\; \u2013\; 3\; =\; -3f(1)\; =\; 2(1)\; \u2013\; 3\; =\; -1`frac\{f(0)+f(1)\}\{2\}=\backslash frac\{-3-1\}\{2\}=\backslash frac\{-4\}\{2\}`(ii)\; f(x)\; =\; 0\Rightarrow \; 2x\; \u2013\; 3\; =\; 02x\; =\; 3x\; =\; `frac\{3\}\{2\}`(iii)\; f(x)\; =\; x\Rightarrow \; 2x\; \u2013\; 3\; =\; x\; \Rightarrow \; 2x\; \u2013\; x\; =\; 3x\; =\; 3(iv)\; f(x)\; =\; f(1\; \u2013\; x)2x\; \u2013\; 3\; =\; 2(1\; \u2013\; x)\; \u2013\; 32x\; \u2013\; 3\; =\; 2x\; \u2013\; 2x\; \u2013\; 32x\; +\; 2x\; =\; 2\; \u2013\; 3\; +\; 34x\; =\; 2x\; =\; `frac\{2\}\{4\}`x=\; `frac\{1\}\{2\}`Question\; 7.An\; open\; box\; is\; to\; be\; made\; from\; a\; square\; piece\; of\; material,\; 24\; cm\; on\; a\; side,\; by\; cutting\; equal\; squares\; from\; the\; corners\; and\; turning\; up\; the\; sides\; as\; shown\; in\; figure.\; Express\; the\; volume\; V\; of\; the\; box\; as\; a\; function\; of\; x.$ \frac{\mathrm{Solution:}}{}$Volume\; of\; the\; box\; =\; Volume\; of\; the\; cuboid=\; l\; \times \; b\; \times \; h\; cu.\; unitsHere\; l\; =\; 24\; \u2013\; 2xb\; =\; 24\; \u2013\; 2xh\; =\; x\therefore \; V\; =\; (24\; \u2013\; 2x)\; (24\; \u2013\; 2x)\; \times \; x=\; (576\; \u2013\; 48x\; \u2013\; 48x\; +\; 4x\xb2)xV\; =\; 4x\xb3\u2013\; 96x\xb2+\; 576x$ \frac{\mathrm{Question\; 8.}}{}$A\; function\; f\; is\; defined\; bv\; f(x)\; =\; 3\; \u2013\; 2x\; .\; Find\; x\; such\; that\; f(x2)\; =\; (f(x))2.$ \frac{\mathrm{Solution:}}{}$f(x)\; =\; 3\; \u2013\; 2xf(x\xb2)\; =\; 3\; \u2013\; 2x\xb3$ \frac{\mathrm{Question\; 9.}}{}$A\; plane\; is\; flying\; at\; a\; speed\; of\; 500\; km\; per\; hour.\; Express\; the\; distance\; d\; travelled\; by\; the\; plane\; as\; function\; of\; time\; r\; in\; hours.$ \frac{\mathrm{Answer:}}{}$Speed\; of\; the\; plane\; =\; 500\; km/hrDistance\; travelled\; in\; \u201ct\u201d\; hours=\; 500\; \times \; t\; (distance\; =\; speed\; \times \; time)=\; 500\; t$ \frac{\mathrm{Question\; 10.}}{}$The\; data\; in\; the\; adjacent\; table\; depicts\; the\; length\; of\; a\; woman\u2019s\; forehand\; and\; her\; corresponding\; height.\; Based\; on\; this\; data,\; a\; student\; finds\; a\; relationship\; between\; the\; height\; (y)\; and\; the\; forehand\; length(x)\; as\; y\; =\; ax\; +\; b,\; where\; a,\; b\; are\; constants.(i)\; Check\; if\; this\; relation\; is\; a\; function.(ii)\; Find\; a\; and\; b.(iii)\; Find\; the\; height\; of\; a\; woman\; whose\; forehand\; length\; is\; 40\; cm.(iv)\; Find\; the\; length\; of\; forehand\; of\; a\; woman\; if\; her\; height\; is\; 53.3\; inches.$ \frac{\mathrm{Solution:}}{}$(i)\; Given\; y\; =\; ax\; +\; b\; \dots \dots \dots \dots .\; (1)The\; ordered\; pairs\; are\; R\; =\; \{(35,\; 56)\; (45,\; 65)\; (50,\; 69.5)\; (55,\; 74)\}\therefore \; Hence\; this\; relation\; is\; a\; function.\Rightarrow \; 65\; =\; 45(.9)\; +\; b\Rightarrow \; 65\; =\; 40.5\; +\; b\Rightarrow \; b\; =\; 65\; \u2013\; 40.5\Rightarrow \; b\; =\; 24.5\therefore \; a\; =\; 0.9,\; b\; =\; 24.5\therefore \; y\; =\; 0.9x\; +\; 24.5(iii)\; Given\; x\; =\; 40\; ,\; y\; =\; ?\therefore \; (4)\; \to \; y\; =\; 0.9\; (40)\; +\; 24.5\Rightarrow \; y\; =\; 36\; +\; 24.5\Rightarrow \; y\; =\; 60.5\; inches(iv)\; Given\; y\; =\; 53.3\; inches,\; x\; =\; ?(4)\; \to \; 53.3\; =\; 0.9x\; +\; 24.5\Rightarrow \; 53.3\; \u2013\; 24.5\; =\; 0.9x\Rightarrow \; 28.8\; =\; 0.9x\Rightarrow \; x\; =\; `frac\{28.8\}\{0.9\}`\; =32\; cm\therefore \; When\; y\; =\; 53.3\; inches,\; x\; =\; 32\; cm}}{}$

Thanks for giving the valuable post

ReplyDeleteWow, excellent post. I'd like to draft like this too - taking time and real hard work to make a great article. This post has encouraged me to write some posts that I am going to write soon. exercise books

ReplyDelete