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MTH202 Assignment 2 Solution - Function Domain, Bijective Function, Geometric Sequence, Exercises of Mathematics

Institute of Mathematical Sciences Mathematics

The solutions to assignment 2 of mth202 (spring 2012) which includes finding the domain and range of a function, proving if a function is bijective, and determining the 15th term of a geometric sequence.

Typology: Exercises

2011/2012

Uploaded on 08/03/2012

roocky 🇮🇳

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Solution Of Assignment 2 Of MTH202 (Spring 2012)

Maximum Marks: 15

Question 1; Mark: 5

If



52 2 xxf and



5 xxg then find the domain and range of



xfog ?

Solution:

 







52

552

5

2







x

xfxgfxfog

  

 ,xfofDom



),5[ xgofDom



),5[),5[),(











xfogofDomain



),5[ xfofRange



),0[ xgofRange



),5[),5[),0[





xfogofRange

Question 2; Marks: 6

Define RZg : by the rule



Zxxxg  ,59

Is



xg bijective function? Prove or disprove.

Solution:

For bijective function we shall prove that g(x) is one to one and onto.

  

21

99

5959

xx

xgxgLet







So g(x) is one to one function.

Now we show that g(x) is onto function.

9

5

59







y

x

y

Let

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Download MTH202 Assignment 2 Solution - Function Domain, Bijective Function, Geometric Sequence and more Exercises Mathematics in PDF only on Docsity!

Solution Of Assignment 2 Of MTH202 (Spring 2012)

Maximum Marks: 15

Question 1; Mark: 5

If f   x  2 x^2  5 and g   x  x  5 then find the domain and range of  fog  x?

Solution:

2

x

fogx f gx f x

Dom of f   x   ,

Dom of g   x [ 5 ,)

Domainof  fog  x ( ,)[ 5 ,)[ 5 ,)

Range of f   x [ 5 , )

Range of g   x [ 0 ,)

Rangeof  fog  x [ 0 ,)[ 5 ,)[ 5 ,)

Question 2; Marks: 6

Define g : Z  R by the rule

g   x  9 x  5 ,  x  Z

Is g   x bijective function? Prove or disprove.

Solution: For bijective function we shall prove that g(x) is one to one and onto.

1 2

x x

Let g x gx

So g(x) is one to one function. Now we show that g(x) is onto function.

y x

Let y x

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This is not always an integer, so g(x) is not onto function. Counter Example: Consider  

x Z

x

g x

Hence g(x) is not bijective function.

Question 3; Marks: 4

Find the 15th^ term of the given sequence  9 , 27 , 81 ,.....

Solution: This is a geometric sequence where a   9 r  3 n  15 So 15th^ term of the sequence is

   43046721

1

a

a (^) n arn

MTH202 Assignment 2 Solution - Function Domain, Bijective Function, Geometric Sequence, Exercises of Mathematics

Related documents

Partial preview of the text

Download MTH202 Assignment 2 Solution - Function Domain, Bijective Function, Geometric Sequence and more Exercises Mathematics in PDF only on Docsity!

Solution Of Assignment 2 Of MTH202 (Spring 2012)

If f   x  2 x^2  5 and g   x  x  5 then find the domain and range of  fog  x?

Dom of f   x   ,

Dom of g   x [ 5 ,)

Domainof  fog  x ( ,)[ 5 ,)[ 5 ,)

Range of f   x [ 5 , )

Range of g   x [ 0 ,)

Rangeof  fog  x [ 0 ,)[ 5 ,)[ 5 ,)

g   x  9 x  5 ,  x  Z

Is g   x bijective function? Prove or disprove.

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