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Class 11-commerce RD SHARMA Solutions Maths Chapter 3: Functions

Functions Exercise Ex. 3.1

Solution 1


Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

  

Functions Exercise Ex. 3.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5


Solution 6

Solution 7


Solution 8

Solution 9(i)

  

Solution 10

Solution 9(ii)

 

 

  

Solution 11

Functions Exercise Ex. 3.3

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 2

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 3(iv)

Solution 3(v)

Solution 3(vi)

Solution 3(viii)

Solution 3(vii)

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.

Functions Exercise Ex. 3.4

Solution 1(i)

Solution 1(ii)

Solution 2

Solution 3

Solution 4(i)

Solution 4(ii)

Solution 4(iii)

Solution 4(iv)

Solution 4(v)

Solution 4(vi)

Solution 4(vii)

Solution 4(viii)

Solution 5

Solution 6

Solution 7


Solution 8

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

Solution 9

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 ;

Solution 10

 

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

Functions Exercise Ex. 3VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14