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Relations and Functions Test - 6

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Relations and Functions Test - 6
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Weekly Quiz Competition
  • Question 1
    1 / -0
    A relation R on a non-empty set A is an equivalence relation, if it is
  • Question 2
    1 / -0

    If f (x) =√−x, then domain of fof is


    Solution

    √fx   is defined only if

    f(x)will be non negative.

    Hence ∴√−f(x)is defined only for 0.

  • Question 3
    1 / -0
    In the relation R : A → B, where A = {1, 2, 3, 4, 5} and B = {u, v, x, y, z} is a function, R is given by
  • Question 4
    1 / -0

    Let x be any real, then [x + y] = [x] + [y] holds for

    Solution

    [x]=x  ∀ x∈I

    so,

    [x+y]=[x]+[y] only if x and y ∈ I

  • Question 5
    1 / -0
    If f : R is defined by f(x) = x2 - 6x - 14, then f-1(2) is equal to
  • Question 6
    1 / -0
    Number of relation that can be defined on a set A = (a, b, c, d) is
  • Question 7
    1 / -0
  • Question 8
    1 / -0
    If f : R → R is given by f(x) = x2 - 3, then f -1 is given by
  • Question 9
    1 / -0
    The domain of definition of the function y(x) given by the equation 2x + 2y = 2 is
  • Question 10
    1 / -0
    If

    then gof is equal to
  • Question 11
    1 / -0
    The diagram given below shows that

  • Question 12
    1 / -0
    Let f(x) =  then (fofof) (x) equals to
  • Question 13
    1 / -0
    The number of one-to-one functions from a set containing m elements to another set containing n elements is:
  • Question 14
    1 / -0
    The function f(x) = , is
  • Question 15
    1 / -0
    If f(x) =  is defined as [0, )  [0, ), then f(x) is
  • Question 16
    1 / -0
    If f : R ⇒ R is defined as f(x) = x2 - 3x + 4 for all x ∈ R, then f-1 (2) is equal to
  • Question 17
    1 / -0
    The function f : R - {2} R defined by is
  • Question 18
    1 / -0

    The function f (x) = x + cos x


    Solution

    f(x)=x;g(x)=cosx

    Df=R

    Dg=R

    Df+g=Df∩Dg 

    so,

    Df+g=R

    SO given function is defined for all reals

  • Question 19
    1 / -0
    Let A = {1, 2, 3}. The total no. of distinct relations which can be defined over A is
  • Question 20
    1 / -0

    The function f (x) = x + cos x

    Solution

    f(x)=x;g(x)=cosx

    Df=R

    Dg=R

    Df+g=Df∩Dg 


    so,

    Df+g=R


    SO given function is defined for all reals

  • Question 21
    1 / -0
    If f : I → I be defined by f(x) = x + i, where i is a fixed integer, then f is
  • Question 22
    1 / -0
    If f : R - {3} R - {1} is defined by f(x) = , then f is
  • Question 23
    1 / -0
    If A = {1, 2, 3}, B = {4, 5, 6}, which of the following is a relation from A to B?
  • Question 24
    1 / -0
    If f(x) = , then at x = 0, f has
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