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CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 4 - MCQExams.com

If f(x)={x+1,ifx15x2ifx>1,g(x)={xifx12xifx>1

and x(1,2), then g(f(x)) is equal to
  • x2+3
  • x23
  • 5x2
  • 1x
Which of the functions defined below are NOT one-one function(s) 
  • f(x)=5(x2+4),(xR)
  • g(x)=2x+1x
  • h(x)=ln(x2+x+1),(xR)
  • f(x)=ex
If g(x)=2x+1 and h(x)=4x2+4x+7, find a function f such that fog=h
  • f(x)=x36
  • f(x)=x2+6
  • f(x)=x26
  • f(x)=(2x+1)2+6
Which of the following are two distinct linear functions which map the interval [1,1] onto [0,2]
  • f(x)=1+x or 1x
  • f(x)=1+2x or 1x
  • f(x)=1+x or 12x
  • f(x)=1+x or 2x
Which of the following is an onto function
  • f:[0,π][11],f(x)=sinx
  • f:[0,π][1,1],f(x)=cosx
  • f:RR,f(x)=ex
  • f:QR,f(x)=x3
If f:RR,f(x)=(x+1)2 and g:RR,g(x)=x2+1 then (fog)(3) is equal to
  • 121
  • 144
  • 112
  • 11
If f(x)=logx, g(x)=x3, then f[g(a)]+f[g(b)] equals
  • f[g(a)+g(b)]
  • 3f(ab)
  • g[f(ab)]
  • g[f(a)+f(b)]
If f(x)=x3 and g(x)=sin2x, then
  • g[f(1)]=1
  • f(g(π/12)=1/8
  • gf(2)=sin2
  • none of these
If f(x)=(axn)1/n, where  nN, then f{f(x)} equals
  • 0
  • x
  • xn
  • none of these
The domain of the function ln(x1) is.
  • [0,1)
  • R
  • RZ
  • (1,)
If f(x)=ln1+x1x and g(x)=3x+x31+3x2, then f[g(x)] equals.

  • f(x)
  • [f(x)]3
  • 3f(x)
  • f(x)2
If f(x)={1xQ0xQ then fof(3) is equal to
  • 0
  • 1
  • 3
  • none of these
Let f(x)=e3x,g(x)=logex,x>0, then fog(x) is
  • 3x
  • x3
  • log103x
  • log3x
f(x)>x;xϵR. The equation f(f(x))x=0 has
  • Atleast one real root
  • More than one real root
  • No real root if f(x) is a polynomial & one real root if f(x) is not a polynomial
  • No real root at all
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
The domain of the function,  y=f(x)=log10(5xx24) is
  • [1,4]
  • (1,4)
  • [1,4)
  • (1,4]
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)=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(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
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
The domain of the function, f(x)=1[x]2[x]6  is
  • (,3][4,)
  • (,2)[4,)
  • (,2)(4,)
  • none of these
The domain of the function f(x)=log0.3(x1)x2+2x+8 is
  • (1,4)
  • (2,4)
  • [2,4)
  • none of these
If f:[0,Π][1,1], f(x) = cosx, then f is.
  • one-one
  • onto
  • one-one onto
  • none of these
The domain of the function f(x)=111x2 is .
  • (,1)
  • (1,)
  • [0,1]
  • [1,1]
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
If f(x)=(1x3)13, then find fof(x)
  • 1x
  • x
  • x2
  • x3
f:AB defined by f(x) = 2x+3 and if A = {-2,-1,0,1,2} B = {-1,1,3,5,7} then which type of function is f?
  • One-one
  • Onto
  • Bijection
  • Constant
The domain of the function f(x)=1x3 is
  • x<3
  • x>3
  • x3
  • x3
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)
The domain of the function f(x) = log [x-1] is_______
  • R - {1,-1}
  • R - {1}
  • R - {-1}
  • R - {0}
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
If f(x)=x2+1,g(x)=3x then (gofogofogogog) (x) is.
  • an odd function
  • an even function
  • a polynomial function
  • an identity function
The domain of the function, f(x)=|x|2|x|3 is ..........
  • R
  • R{2,3}
  • R{2,2}
  • R{3,3}
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
Find (fg)(3) when f(x)=7x6 and g(x)=5x27x6.
  • 36
  • 1014
  • 90
  • 120
If f is a constant function and f(100)=100  then f(2007)=_____
  • 2007
  • 100
  • 0
  • None of these
If f(x)=(pxn)1/n,p>0 and n is a positive integer, then f(f(x))=
  • x
  • xn
  • p1/n
  • pxn
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}
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
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
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
The domain of the function f(x)=log(1x)+x21
  • (,1)
  • (,1]
  • (,2]
  • (,0)
If h(x)=x3+x and g(x)=2x+3, then calculate g(h(2)).
  • 7
  • 10
  • 17
  • 19
  • 23
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
Find the correct expression for f(g(x)) if f(x)=4x+1 and g(x)=x22  
  • x2+4x+1
  • x2+4x1
  • 4x27
  • 4x21
  • 16x2+8x1
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
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers