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2 Let N be the set of natural numbers. D...

2 Let N be the set of natural numbers. Define a real valued function f : N-> N by f (x) = 2x + 1. Using this definition, complete the table given below.

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Given function is `f(x)=2x+1`
so,
`f(1)=>2(1)+1=3`
`f(2)=>2(2)+1=5`
`f(3)=>2(3)+1=7`
`f(4)=>2(4)+1=9`
`f(5)=>2(5)+1=11`
`f(6)=>2(6)+1=13`
...
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Knowledge Check

  • The function f N rarr N. where N being the set of natural numbers, defined by f(x) = 2x + 3 is:

    A
    Injective and surjective
    B
    Injective but not surjective
    C
    Not injective hut surjective
    D
    Neither injective nor surjective
  • Let N be the set of natural numbers and f: N rarr N be a function given by fox)=x+1 for x ne N. Which one of the following is correct?

    A
    A. f is one-one and onto
    B
    B. f is one-one but not onto
    C
    C. f is only onto
    D
    D. f is neither one-one nor onto
  • Let N be the set of natural numbers and the relation R be defined such that R = {(x,y):y = 2x,x,y in N} Then,

    A
    R is a function
    B
    R is not a function
    C
    domain range and codomain is N
    D
    None of the above
  • NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
    1. 2 Let N be the set of natural numbers. Define a real valued function f...

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    2. Examine each of the following relations given below and state in each ...

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    3. Define the function f : R ->R by y = f(x) = x^2, x in R. Complete ...

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    4. Let N be the set of natural numbers and the relation R be defined on ...

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    5. Let f(x)=sqrt(x)and g(x) = xbe two functions defined over the set of ...

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    6. Let f(x)=x^2and g(x) = 2x + 1be two real functions. find (f +g)(x),...

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    7. Define the real valued function f : R {0} ->Rdefined by f(x)=1/x,...

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    8. Draw the graph of the function f : R-> Rdefined by f(x)=x^3, x in R...

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    9. Let R be a relation from Q to Q defined by R={(a,b):a,b in Q and a,b i...

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    10. Let R be the set of real numbers. Define the real function f : R ->Rb...

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    11. If (x + 1, y - 2) = (3, -1), find the values of x and y.

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    12. Let A= {1, 2, 3}, B = {3, 4}and C = {4, 5, 6}. Find(i) A xx(B nnC...

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    13. If P = {a , b , c}and A xxB = {(p , q), (p , r), (m , q), (m , r)}Q = ...

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    14. If R is the set of all real numbers, what do the cartesian products R...

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    15. If P = {1, 2}form the set P xxP xxP.

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    16. The function f is defined by f(x) ={[1-x \ x<0], [1 \ \ \ \ \ \ \ \ ...

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    17. Find the domain of the function f(x) =(x^2-3x+5)/(x^2-5x+4).

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    18. Let f = {(1, 2), (2, 3), (0, -1), ( -1, -3)} be a linear function ...

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    19. If A xxB = {(p , q), (p , r), (m , q), (m , r)}, find A and B.

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    20. Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x...

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