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CBSE Questions for Class 12 Commerce Maths Relations And Functions Quiz 5 - MCQExams.com

If f(x)=11x,x0,1 then the graph of the function y=f[f{f(x)}] for x>1  is
  • a straight line
  • a circle
  • an ellipse
  • a pair of straight lines
Let f:RR,g:RR be two function such that
f(x)=2x3,g(x)=x3+5
The function (fog)1(x) is equal to.
  • (x+72)1/3
  • (x72)1/3
  • (x27)1/3
  • (x72)1/3
If f(x)=3x5,thenf1(x).
  • is given by 13x5
  • is given by x+53
  • does not exist because f is not one-one
  • does not exist because f is not onto
If f:[0,Π][1,1], f(x) = cosx, then f is.
  • one-one
  • onto
  • one-one onto
  • none of these
If f(x)={1xQ0xQ then fof(3) is equal to
  • 0
  • 1
  • 3
  • none of these
If functions f(x) and g(x) are defined on RR such that
f(x)=x+3,x rational
         =4x,x irrational
g(x)=x+5, x irrational
      =x,x rational
then (fg)(x) is
  • one-one & onto
  • neither one-one nor onto
  • one-one but not onto
  • onto but not one-one
If f(x)=(1x3)13, then find fof(x)
  • 1x
  • x
  • x2
  • x3
Let f(x)=ax+bcx+d. Then fof(x) = x provided that.
  • d =- a
  • d = a
  • a = b = c = d = 1
  • a = b = 1
If f(x)=2x3+7x5andg(x)=f1(x) then g' (4) is equal to
  • 113
  • 1103
  • 14
  • non existent
If R=R1 then the relation R is ________
  • reflexive
  • symmetric
  • anti-symmetric
  • transitive
Let f(x)=32+x34 be a function and g(x) be another function such that g(f(x))=x, then the value of g(20) will be
  • 333
  • 335
  • 338
  • 343
If f(x) + f(1-x) = 10 then the value of f(110)+f(210)+.........+f(910)
  • is 45
  • is 50
  • is 90
  • Cannot be determined
If f(x)=2x1 and g(x)=3x+2, then find (fog)(x) :
  • 2(3x+1)
  • 2(3x+2)
  • 3(2x+1)
  • 3(3x+1)
If f(x)=x2+1,g(x)=3x then (gofogofogogog) (x) is.
  • an odd function
  • an even function
  • a polynomial function
  • an identity function
If the function f(x)=x3+ex/2 and g(x)=f1(x); then the value of g'(1) is
  • 2
  • 2
  • 1
  • 0
If f(x)=2x-1 and g(x)=3x+2  then find (fog) (x)
  • 2(3x+1)
  • 2(3x+2)
  • 3(2x+1)
  • 3(3x+1)
If f(x) = 2x+1 and g(x) = 3x-5 then find (fog)1(0)
  • 5/3
  • 3/2
  • 2/3
  • 3/5
If X = {2,3,5,7,11} and Y = {4,6,8,9,10} then find the number of one-one functions from X to Y
  • 720
  • 120
  • 24
  • 12
Find (fg)(3) when f(x)=7x6 and g(x)=5x27x6.
  • 36
  • 1014
  • 90
  • 120
If R is a relation from a set A to the set B and S is a relation from B to C, then the relation SoR
  • is from C to A
  • does not exist
  • is from A to C
  • None of these
If f = {(1,3) (2,1) (3,4) (4,2)} and g = {(1,2) (2,3) (3,4) (4,1)} then find n(fog)
  • 12
  • 16
  • 4
  • 5
What is the relation for the following diagram?

456168.PNG
  • R={(2,5),(2,6),(3,7)}
  • R={(1,5),(2,6),(3,7)}
  • R={(1,5),(2,6),(1,7)}
  • R={(1,5),(2,6),(2,7)}
Which of the following do(es) not belong to A×B for the sets A={1,2} and B={0,2}?
  • R={(1,0),(2,2)}
  • R={(1,1),(2,1)}
  • R={(1,0),(1,2)}
  • R={(1,2),(2,2)}
What is the relation for the set A={1,0,3} and B={1,2,3} ?
  • R={(1,1),(1,2),(3,3)}
  • R={(1,1),(0,2),(3,3)}
  • R={(1,1),(2,2),(3,3)}
  • R={(1,1),(0,2),(1,3)}
If f:RR be given by f(x)=(3x3)1/3, then find f(f(x)) is

  • x1/3
  • x3
  • x 
  • 3x3
If f:RR and g:RR are defined by f(x)=|x| and g(x)=[x3] for xR, then
g(f(x)):{85<x<85} is equal to
[.] is Greatest integer function
  • {0,1}
  • {1,2}
  • {3,2}
  • {2,3}
If R be the set of all real numbers and f:RR is given by f(x)=3x2+1. Then, the set f1([1,6]) is
  • {53,0,53}
  • [53,53]
  • [13,13]
  • (53,53)
Let R be the set of real numbers and the functions f:RR and g:RR be defined by f(x)=x2+2x3 and g(x)=x+1. Then the value of x for which f(g(x))=g(f(x)) is
  • 1
  • 0
  • 1
  • 2
Let f:RR be such that f is injective and f(x)f(y)=f(x+y) for all x,yR, if f(x),f(y) and f(z) are in GP, then x,y and z are in
  • AP always
  • GP always
  • AP depending on the values of x,y and z
  • GP depending on the values of x,y and z
Find the number of binary operations on the set {a,b} 

  •  10
  • 16
  • 20
  • 8
Let Q be the set of all rational numbers in [0, 1] and f:[0,1][0,1] be defined by f(x)={xforxQ1xforxQ
Then the set S={x[0,1]:(fof)(x)=x} is equal to
  • [0, 1]
  • Q
  • [0, 1] - Q
  • (0, 1)
If f(x)=2100x+1,g(x)=3100x+1, then the set of real numbers x such that f{g(x)}=x is
  • empty
  • a singleton
  • a finite set with more than one element
  • infinite
In three element group {e,a,b} where e is the identity, a5b4 is equal to 
  • a
  • e
  • ab
  • b
Find the value of f1(1.5) if f(x)=3x3+1.
  • 3.4
  • 2.4
  • 1.3
  • 1.5
If f(x)=(pxn)1/n,p>0 and n is a positive integer, then f(f(x))=
  • x
  • xn
  • p1/n
  • pxn
Which of the following is a subgroup of the group G={1,2,3,4,5,6} under 7.
(7: under multiplication modulo 7)
  • {2,6,1}
  • {1,2,4}
  • {5,4,2}
  • {2,3,1}
If f:RR+ and g:R+R are such that g(f(x))=|sinx| and f(g(x))=(sinx)2, then a possible choice for f and g is
  • f(x)=x2,g(x)=sinx
  • f(x)=sinx,g(x)=|x|
  • f(x)=sin2x,g(x)=x
  • f(x)=x2,g(x)=x
If Q1 is the set of all relations other than 1 with the binary operation  defined by ab=a+bab for all a,bQ1, then the identity in Q1 with respect to Q1 is
  • 1
  • 0
  • 1
  • 2
In Z, the set of all integers, the inverse of 7 w.r.t. defined by a×b=a+b+7 for all a,b,Z is : 
  • 14
  • 7
  • 14
  • 7
f(x)=x2+d and g(x)=2x2, where d is a constant. If f(g(2))f(2)=4, find the value of d.
  • 16
  • 5
  • 22
  • 18
If f(g(a))=0  where g(x)=x4+2 and f(x)=|x23|, find the possible value of a.
  • 8+43
  • (8+43)
  • 6
  • 18
If p(x) = \dfrac{x}{x-2} and q(x) = \sqrt{9-x}, find the value of (p\circ  q)(5)
  • 0
  • \dfrac{8}{7}
  • 2
  • Undefined
If f(x) = \sqrt{x} and g(x) = \sqrt{x^2+4}, calculate the value of f(g(2)).
  • 0
  • 1.41
  • 1.68
  • 2.45
  • 2.83
If f(x) = 2x and f(f(x)) = x + 1, then the value of x is
  • \dfrac {1}{3}
  • 1
  • 2
  • 3
  • 5
Find the value of  g(f(2)), if f(x) = e^{x} and g(x) = \dfrac {x}{2}
  • 2.7
  • 3.7
  • 4.2
  • 5.4
  • 6.1
If h(x)={x}^{3}+x and g(x)=2x+3, then calculate g(h(2)).
  • 7
  • 10
  • 17
  • 19
  • 23
If f(x) = x^{2} - 10 and g(x) = 4x + 3, calculate the value of f(g(2)).
  • -24
  • -21
  • 12
  • 27
  • 111
If f(x) = x^2 and g(x) = 2x, calculate the value of f(g(-3))-g(f(-3)).
  • 54
  • 18
  • 0
  • -18
  • -54
The above figure shows the graph of the function f(x), the value of f(f(3)) is:
493615.jpg
  • -4
  • -2
  • 0
  • 1
  • 3
Find the correct expression for \displaystyle f\left( g\left( x \right)  \right)  if \displaystyle f(x)=4x+1 and \displaystyle g\left( x \right) ={ x }^{ 2 }-2  
  • \displaystyle -{ x }^{ 2 }+4x+1
  • \displaystyle { x }^{ 2 }+4x-1
  • \displaystyle 4{ x }^{ 2 }-7
  • \displaystyle 4{ x }^{ 2 }-1
  • \displaystyle 16{ x }^{ 2 }+8x-1
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers