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CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 6 - MCQExams.com

Let f:RR be defined by f(x)=x4 then
  • f may be one-one and onto
  • f is one-one and onto
  • f is one-one but not onto
  • f is neither one-one nor onto
If f:[0,)[0,) and f(x)=x1+x, then f is 
  • One-one and onto
  • One-one but not onto
  • Onto but not one-one
  • Neither one-one nor onto
The function f:AB given by f(x)=x,xA, is one to one but not onto. Then;
  • BA
  • A=B
  • AB
  • AB
  • AB=ϕ
The domain of definition of function f(x)=1+2(x+4)0.52(x+4)0.5+(x+4)0.5+4(x+4)0.5 is
  • R
  • (4,4)
  • R+
  • (4,0)(0,)
If fog=|sinx| and gof=sin2x, then f(x) and g(x) are
  • f(x)=sinx,g(x)=x2
  • f(x)=|x|,g(x)=sinx
  • f(x)=x,g(x)=sin2x
  • f(x)=sinx,g(x)=x2
The domain of the function f(x)=sin1(x+52) is :
  • [1.1]
  • [2,3]
  • [3,7]
  • [7,3]
  • (,)
Let f(x)=|x2|, where x is a real number. Which one of the following is true?
  • f is periodic
  • f(x+y)=f(x)+f(y)
  • f is an odd function
  • f is not one-one function
  • f is an even function
If A={1,3,5,7} and B={1,2,3,4,5,6,7,8} then the number of one-to-one functions from A into B is 
  • 1340
  • 1860
  • 1430
  • 1880
  • 1680
If f(x)=3x+5 and g(x)=x21, then (fg) (x21) is equal to
  • 3x43x+5
  • 3x46x2+5
  • 6x4+3x2+5
  • 6x46x+5
  • 3x2+6x+4
If g(x)=1+x and f{g(x)}=3+2x+x, then f(x) is equal to
  • 1+2x2
  • 2+x2
  • 1+x
  • 2+x
If f(x) and g(x) are two functions with g(x)=x1x and fg(x)=x31x3, then f(x) is equal to
  • 3x2+3
  • x21x2
  • 1+1x2
  • 3x2+3x4
If f:R{1,k}R{α,β} is a bijective function defined by f(x)=(2x1)(2x24px+p3)(x+1)(x2p2x+p2) (where p0), then identify which of the following statement(s) is (are) correct?
  • If kϵ(1,1) then α+β=2
  • If kϵ(1,3) then α+β=6
  • If kϵ(1,3) then α+β=4
  • If kϵ(1,1) then α+β=6
If f(x)=|x|,xR, then
  • f(x)=(f×f)(x)
  • f(x)=x
  • f(x)=(f×f)(x2)
  • f(x)=(ff)(x)
If g(x)=x2+x2 and 12(gf)(x)=2x25x+2, then f(x) is
  • 2x3
  • 2x+3
  • 2x2+3x+1
  • 2x2+3x1
If (ax2+bx+c)y+ax2+bx+c=0, then the condition that x may be a rational function of y is
  • (acac)2=(abab)(bcbc)
  • (abab)2=(abac)(bcbc)
  • (bcbc)2=(abab)(acac)
  • None of these
If f(x)=sin2x+sin2(x+π3)+cosxcos(x+π3) and g(54)=1, then gf(x) is equal to
  • 0
  • 1
  • sin1o
  • None of these
If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x))
  • f(a)=g(c)
  • f(b)=g(b)
  • f(d)=g(b)
  • f(x)=g(a)
Number of solution of the equation  f(x)=g(x)  are same as number of point of intersection of the curves y=f(x)  and  y=g(x)  hence answer the following question.
Number of the solution of the equation  2x=|x1|+|x+1|  is
  • 0
  • 1
  • 2
The domain of definition of the function y(x) given by the equation ax+ay=a(a>1) is
  • 0<x1
  • 0 x<1
  • <x<1
  • <x0.
Let f(x)=x33x+1. The number of different real solutions of f(f(x))=0
  • 2
  • 4
  • 5
  • 7
The domain of the function f(x)=cos1(1|x|2) is
  • (,3)(3,)
  • [3,3]
  • (,3][3,)
  • ϕ
 If f:RR, g:RR are defined byf(x)=5x3, g(x)=x2+3, then (gof1)(3)=
  • 253
  • 11125
  • 925
  • 25111
If the real-valued function f(x)=px+sinx is a bijective function, then the set of all possible values of pϵR is?
  • R{0}
  • R
  • (0,)
  • None of these
f,g:RR are functions such that f(x)=3xsin(πx2),g(x)=x3+2xsin(πx2)
The value of ddxf1(g1(x))x=12 is equal to
  • 230+x
  • 230x
  • 23(28π)
  • 23(28+π)
The graph of a constant function f(x)=k is?
  • A straight line parallel to X-axis
  • A straight line parallel to Y-axis
  • A straight line passing through orgin
  • None
If f,g,h are three functions from a set of positive real numbers into itself satisfying the condition,
f(x)g(x)=hx2+y2 such that x,yϵ(0,).then, f(x)g(x) is a?
  • Constant function
  • Identity function
  • Zero function
  • Signum function
A constant function is a periodic function.
  • True
  • False
If f:RR and g:RR are defined f(x)=x[x] and g(x)=[x]xϵR,f(g(x)).
  • x
  • 0
  • f(x)
  • g(x)
Find number of all such function y=f(x) which are onto?
  • 243
  • 93
  • 150
  • None of these
On differentiating an identity function, we get?
  • Signum function
  • Sinc function
  • Constant function
  • None
Find the domain of definition of f(x)=log2(x+3)x2+3x+2.
  • (3,)
  • {1,2}
  • (3,){1,2}
  • (,)
If f(x1)=f(x2)x1=x2x1,x2ϵA, then what type of a function is f:AB?
  • One-one
  • Constant
  • Onto
  • Many one
If g(x)x2x+1andf(x)=1xx, then-
  • Domain of f(g(x)) ids[0,1]
  • Range of f(g(x)) is (0,723)
  • f (g(x)) is many -one function
  • f(g(x)) is unbounded function
The domain of the function f(x)=1|x|x is
  • (0,)
  • (,0)
  • (,){0}
  • (,)
If A = {1, 3, 5, 7} , B = {2, 4, 6, 8, 10} and let R = {(1,8), (3,6), (5,2), (1,4)} be a relation from A to B. Then,
Domain (R) = ?
  • {1,3,5}
  • {8,6,2,4}
  • {1,2,3,4}
  • None of these
Consider the following functions are odd function in their default domains
(i) 2x12x+1
(ii) x2+1xsinx
(iii) ln(1+x1x)
(iv) xe|x|+cosx
Which of these is/are odd
  • (i) and (iii)
  • (i) and (iv)
  • all four
  • (i), (iii) and (iv)
Let f be an injective map with domain {x, y, z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining are false :
f(x)=1,f(y)1,f(z)2. The value of f1(1) is
  • x
  • y
  • z
  • none of these
Let f(x)=[x][x+2]. Find the domain of f(x)
  • xϵR,x is not an integer
  • (,2)[1,)
  • xϵR,x1
  • (,1]
If f(x) is a real valued function, then which of the following is one-one function?
  • f(x)=e|x|
  • f(x)=|ex|
  • f(x)=sinx
  • f(x)=|sinx|
If A={1,2,3} and B={4,5} then the number of function f:AB which is not onto is ______
  • 2
  • 6
  • 8
  • 4
If f:RR,g:RR are defined by f(x)=5x3,g(x)=x2+3, then, (gof1)(3)=
  • 253
  • 11125
  • 925
  • 25111

A function R on the set N of natural numbers is defined as R ={(2n,2n+1):nN
The domain of R= {2, 4, 6, 8,............}
  • True
  • False
Let f:Ab be a function defined by f(x) =1x2
  • f(x) is one-one if A =[0,1]
  • f(x) is onto if B = [0,1]
  • f(x) is one-one if A =[-1 , 0]
  • f(x) is onto if B = [-1,1]
If f:RR,f(x)={1x>00x=01x<0 and g:RR,g(x)=[x], then (fg)(π) is:
  • π
  • 0
  • 1
  • 1
f:(0,)[0,)  defined by f(x)=x2  is 
  • one - one but not onto
  • onto but not one - one
  • bijective
  • neither one - one nor onto
Let f(x)=x2 and g(x)=x (where x>0),then
  • f(g(x))=x
  • g(f(x))=x
  • The least value of f(g(x))+1g(f(x)) is 2
  • The least value of g(f(x))+1f(g(x)) is 2
Let A={1,2,3,4,5,6}. The number of onto functions from A toA such that.f(x)x for all xA is
  • 720
  • 240
  • 245
  • 265
The domain of definition of the function y(x) given by equation 2x+2y=2 is
  • 0<x1
  • 0x1
  • <x0
  • <x<1
The domain of the function f(x)=sin1(log2(x22)) is 
  • [2,1)(1,2]
  • (2,1][1,2]
  • [2,1][1,2]
  • (2,1)(1,2)
If g(x)=x2+x2 and 12gof(x)=2x2+5x+2, then f(x) is
  • 2x3
  • 2x+3
  • 2x2+3x+1
  • 2x23x1
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers