Chapter 3 Functions - RD Sharma Solutions for Class 11-science Mathematics CBSE

Chapter 3 - Functions Exercise Ex. 3.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Express the function f: X ® R given by f (x) = x ³ + 1 as set of ordered pairs, where X = {-1, 0, 3, 9, 7}.

Solution 18

Chapter 3 - Functions Exercise Ex. 3.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

$begin mathsize 12px style If space straight f left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator 1 minus straight x end fraction comma space Show space that space straight f left square bracket straight f left curly bracket straight f left parenthesis straight x right parenthesis right curly bracket right square bracket equals straight x. end style$

Solution 4

Question 5

Solution 5

Question 6

$begin mathsize 11px style Find space colon left parenthesis straight i right parenthesis space straight f space left parenthesis 1 divided by 2 right parenthesis space space left parenthesis ii right parenthesis space straight f left parenthesis negative 2 right parenthesis space space left parenthesis iii right parenthesis space straight f left parenthesis 1 right parenthesis space left parenthesis iv right parenthesis space straight f left parenthesis square root of 3 right parenthesis space and space left parenthesis straight v right parenthesis space straight f left parenthesis square root of negative 3 end root right parenthesis. end style$

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Chapter 3 - Functions Exercise Ex. 3.3

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

find the domain and range of $f open parentheses x close parentheses space equals space square root of 9 minus x squared end root$

Solution 13

Question 14

Find domain and range of f (x) = -|x|

Solution 14

As |x|is defined for all real numbers, its domain is R and range is only negative numbers because, |x| is always positive real number for all real numbers and -|x| is always negative real numbers.

Chapter 3 - Functions Exercise Ex. 3.4

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

$f : R rightwards arrow R space d e f i n e d space b y space left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals 3 x minus 2 f : R rightwards arrow R space d e f i n e d space b y space left parenthesis f minus g right parenthesis left parenthesis x right parenthesis equals minus x plus 4 f : R minus open curly brackets 3 over 2 close curly brackets rightwards arrow R space d e f i n e d space b y space f over g left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator 2 x minus 3 end fraction$

Question 17

Solution 17

$f plus g : left square bracket 0 comma infinity right parenthesis rightwards arrow R space d e f i n e d space b y space left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals square root of x plus x ; space f minus g : left square bracket 0 comma infinity right parenthesis rightwards arrow R space d e f i n e d space b y space left parenthesis f minus g right parenthesis left parenthesis x right parenthesis equals square root of x minus x ; f g : left square bracket 0 comma infinity right parenthesis rightwards arrow R space d e f i n e d space b y space left parenthesis f g right parenthesis left parenthesis x right parenthesis equals x to the power of 3 divided by 2 end exponent ; f over g : left square bracket 0 comma infinity right parenthesis rightwards arrow R space d e f i n e d space b y space open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x end fraction ;$

Question 18

Solution 18

$left parenthesis f plus g right parenthesis : R rightwards arrow left square bracket 0 comma infinity right parenthesis space d e f i n e d space b y space left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals x squared plus 2 x plus 1 equals left parenthesis x plus 1 right parenthesis squared left parenthesis f minus g right parenthesis : R rightwards arrow R space d e f i n e d space b y space left parenthesis f minus g right parenthesis left parenthesis x right parenthesis equals x squared minus 2 x minus 1 open parentheses f g close parentheses : R rightwards arrow R space d e f i n e d space b y space left parenthesis f g right parenthesis left parenthesis x right parenthesis equals 2 x cubed plus x squared open parentheses f over g close parentheses : R rightwards arrow R space d e f i n e d space b y space open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator x squared over denominator 2 x plus 1 end fraction$