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CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 5 - MCQExams.com

If p(x)=xx2 and q(x)=9x, find the value of (pq)(5)
  • 0
  • 87
  • 2
  • Undefined
Consider the functions f(x)=x and g(x)=7x+b. Find the value of b, if the composite function, y=f(g(x)) passes through (4,6)
  • 8
  • 8
  • 25
  • 26
  • 476
In real number system, find the domain of the function f(x)=x3x3.
  • x3
  • x>3
  • x<3
  • x>3
  • x<3 or x>3
If f(x)= x and g(x)= x2+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
  • 13
  • 1
  • 2
  • 3
  • 5
If f(x)=x24, identify its domain.
  • All real numbers
  • All x such that x2
  • All x such that x2
  • All x such that 2x2
  • All x such that x2 or x2
Which of the following is the domain of the function f(x)=3xx29?
  • 3>x>3
  • xx3
  • 3x<3
  • x<3 or x>3
  • x3 or x3
If f(x)= x2 and g(x)=2x, calculate the value of f(g(3))g(f(3)).
  • 54
  • 18
  • 0
  • -18
  • -54
Find g(x), if f(x)=7x+12 and f(g(x)=21x2+40
  • 21x2+28
  • 21x2
  • 7x2+4
  • 3x2+28
  • 3x2+4
If \left\{ \left( 7,11 \right) ,\left( 5,a \right)  \right\} represents a constant function, then the value of 'a' is :
  • 7
  • 11
  • 5
  • 9
Given a function f(x) = \dfrac {1}{2}x - 4 and the composite function f(g(x)) = g(f(x)), determine which among the following can be g(x):
I. 2x - \dfrac {1}{4}
II. 2x + 8
III. \dfrac {1}{2}x - 4
  • I only
  • II only
  • III only
  • II and III only
  • I, II, and III
Find the values of x for which \dfrac {1}{\sqrt {x + 1}} is undefined
  • -1 only
  • 1 only
  • All real numbers greater than -1
  • All real numbers less than -1
  • All real numbers less than or equal to -1
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 f(x) = 4x - 3 and g(x) = x - 4, determine which of the following composite function has a value of -11.
  • f(g(2))
  • g(f(2))
  • g(f(3))
  • f(g(3))
  • f(g(4))
If f(x) = x^{2} - 10 and g(x) = 4x + 3, calculate the value of f(g(2)).
  • -24
  • -21
  • 12
  • 27
  • 111
Find the domain of the function f(x) = \sqrt {x^{2} + 3}.
  • -1.73 \leq x \leq 1.73
  • -1.32 \leq x \leq 1.32
  • x > 1.32
  • x > 1.73
  • All real numbers
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
2 does not lie in the domain of which of the following function?
  • f(x) = \dfrac {x^{2} - 2x}{x^{2} - 2x^{3}}
  • f(x) = \dfrac {x^{-2} - \dfrac {2}{x}}{x^{2} - 2x^{2}}
  • f(x) = \dfrac {2x^{2}}{x^{3} - 2x^{2}}
  • f(x) = \dfrac {x^{2} - 2x}{x^{2} - x}
  • f(x) = \dfrac {4x^{2}}{x^{-2} + 2x}
If f(x) = 3x - 5 and g(x) = x^2 + 1, f [g(x)] =
  • 3x^2-5
  • 3x^2+6
  • x^2-5
  • 3x^2-2
  • 3x^2+5x-2
If k is a positive constant different from 1, which of the following could be the graph of \displaystyle y-x=k(x+y) in the xy-plane?
If g(x) = \dfrac {5x - 3}{2x^{2} - 11 - 6}, what is the sum of all the real numbers that are not in the domain of g(x)?
  • -2
  • 0.5
  • 2
  • 5.5
  • 6.5
The Set A has 4 elements and the Set B has 5 elements then the number of injective mappings that can be defined from A to B is
  • 144
  • 72
  • 60
  • 120
Let f:R\rightarrow R be defined by f(x)=2x+6 which is a bijective mapping then { f }^{ -1 }(x)\quad is given by
  • \cfrac { x }{ 2 } -3
  • 2x+6
  • x-3
  • 6x+2
If f(x)=\dfrac{x+1}{x-1} and g(x)=2x-1, f[g(x)]=
  • \dfrac{x-1}{x}
  • \dfrac{x}{x+1}
  • \dfrac{x+1}{x}
  • \dfrac{x}{x-1}
  • \dfrac{2x-1}{2x+1}
The domain of g(x)=\cfrac { 3 }{ \sqrt { 4-{ x }^{ 2 } }  } is:
  • \left[ -2,2 \right]
  • \left( -2,2 \right)
  • \left( 0,2 \right)
  • \left( -\infty ,-2 \right)
  • \left( -\infty ,2 \right)
Let f : N \rightarrow N defined by f(n)=\left\{\begin{matrix} \dfrac{n+1}{2} & \text{if }\, n \, \text{is odd} \\ \dfrac{n}{2} & \text{if}\, n \, \text{is even} \end{matrix}\right.
then f is.
  • Many-one and onto
  • One-one and not onto
  • Onto but not one-one
  • Neither one-one nor onto
The number of onto functions from the set \{1, 2, .........., 11\} to set \{1, 2, ....., 10\} is
  • 5\times \underline{|11}
  • \underline{|10}
  • \dfrac{\underline{|11}}{2}
  • 10\times \underline{|11}
If f: R\rightarrow R is defined by f(x) = \dfrac {x}{x^{2} + 1}, find f(f(2))
  • \dfrac {1}{29}
  • \dfrac {10}{29}
  • \dfrac {29}{10}
  • 29
The domain of the function f(x)=\sqrt{\cos x} is.
  • \left [ 0, \frac{\pi}{2} \right ]
  • \left [ 0, \frac{\pi}{2} \right ]\cup \left [ \frac{3\pi}{2}, 2\pi \right ]
  • \left [ \frac{3\pi}{2}, 2 \pi \right ]
  • \left [ \frac{-\pi}{2}, \frac{\pi}{2} \right ]
Let f(x)=2x-\sin x and g(x)=\sqrt[3] x, then
  • Range of gof is R
  • gof is one-one
  • both f and g are one-one
  • both f and g are onto
For the function f(x) = \left [\dfrac {1}{[x]}\right ], where [x] denotes the greatest integer less than or equal to x, which of the following statements are true?
  • The domain is (-\infty, \infty)
  • The domain is \left \{0\right \} \cup \left \{-1\right \} \cup \left \{1\right \}
  • The domain is \left (-\infty, 0\right ) \cup [1, \infty)
  • The domain is \left \{0\right \}\cup \left \{1\right \}
If the function f : R \rightarrow R is defined by f(x) = (x^2+1)^{35} \forall \in R, then f is
  • One-one but not onto
  • Onto but not one-one
  • Neither one-one nor onto
  • Both one-one and onto
Let f(x) = 2^{100}x+1
g(x) = 3^{100}x+1
Then the set of real numbers x such that f(g(x)) = x is
  • Empty
  • A singleton
  • A finite se with more than one element
  • Infinite
The number of real linear functions f(x) satisfying f(f(x))=x+f(x) is
  • 0
  • 4
  • 5
  • 2
Let f : R\rightarrow R be defined by f(x) = \dfrac {1}{x} \ \   \forall  \ x \ \in \ R, then f is _____
  • One-one
  • Onto
  • Bijective
  • f is not defined
Consider the function f(x)=\displaystyle\frac{x-1}{x+1}What is f(f(x)) equal to?
  • x
  • -x
  • -\displaystyle\frac{1}{x}
  • None of the above
Let N denote the set of all non-negative integers and Z denote the set of all integers. The function f : Z \rightarrow N given by f(x) = |x| is :
  • One-one but not onto
  • Onto but not one-one
  • Both one-one and onto
  • Neither one-one nor onto
The curve a^{2}y^{2} = x^{2}(a^{2} - x^{2}) is defined for
  • x\leq a and x\geq -a
  • x < a and x > -a
  • x \leq -a and x\geq a
  • x\leq a and x > -a
If f(x) = \log_{e}\left (\dfrac {1 + x}{1 - x}\right ), g(x) = \dfrac {3x + x^{3}}{1 + 3x^{2}} and go f(t) = g(f(t)), then what is go f\left (\dfrac {e - 1}{e + 1}\right ) equal to?
  • 2
  • 1
  • 0
  • \dfrac {1}{2}
If g(x)=\dfrac{1}{f(x)} and f(x)=x, x\ne 0, then which one of the following is correct?
  • f(f(f(g(g(f(x))))))=g(g(f(g(f(x)))))
  • f(g(f(g(g(f(g(x)))))))=g(g(f(g(f(x)))))
  • f(g(f(g(g(f(g(x)))))))=f(g(f(g(f(x)))))
  • f(f(f(g(g(f(x))))))=f(f(f(g(f(x)))))
The domain of the function f(x) = \dfrac {1}{\log_{10}(1 - x)} + \sqrt {x + 2} is
  • [-3, -2.5]\cap[ - 2.5, -2]
  • [-2, 0)\cup(0, 1)
  • [0, 1]
  • None of the above
Let f(x)=\dfrac{x+1}{x-1} for all x \neq 1
Let
f^1(x)=f(x), f^2(x)=f(f(x)) and generally
f^n(x)=f(f^{n-1}(x)) for n > 1
Let P= f^1(2)f^2(3)f^3(4)f^4(5)
Which of the following is a multiple of P ?
  • 125
  • 375
  • 250
  • 147
Number of values of x\in [0, \pi] where f(x) = [4\sin x-7] is non-derivable is
[Note: [k] denotes the greatest integer less than or equal to k.]
  • 7
  • 8
  • 9
  • 10
Let M be the set of all 2 \times 2 matrices with entries from the set of real numbers R. Then the function  f : M \rightarrow R defined by f\left( A \right) =\left| A \right| for every  A\in M, is
  • One-one and onto
  • Neither one-one nor onto
  • One-one but not onto
  • Onto but not one-one
Consider the following statements :
Statement 1 : The function f:R \rightarrow R such that f(x)=x^3 for all x\in R is one-one.
Statement 2 : f(a) = f(b) \Rightarrow a=b for all a, b \in R if the function f is one-one.
Which one of the following is correct in respect of the above statements?
  • Both the statements are true and Statement 2 is the correct explanation of Statement 1.
  • Both the statements are true and Statement 2 is not the correct explanation of Statement 1.
  • Statement 1 is true but Statement 2 is false.
  • Statement 1 is true but Statement 2 is true.
If f(x) = 8x^3, g(x) = x^{1/3}, then fog (x) is
  • 8^3x
  • (8x)^{1/3}
  • 8x^3
  • 8x
The mid-point of the domain of the function f\left( x \right) =\sqrt { 4-\sqrt { 2x+5 }  } for real x is
  • \dfrac{1}{4}
  • \dfrac{3}{2}
  • \dfrac{2}{3}
  • -\dfrac{2}{5}
The domain of the function
f(x)=\sin ^{ -1 }{ \left\{ \log _{ 2 }{ \left( \cfrac { 1 }{ 2 } { x }^{ 2 } \right)  }  \right\}  } is
  • \left[ -2,1 \right] \cup \left[ 1,2 \right]
  • (-2,-1] \cup [1,2]
  • \left[ -2,-1 \right] \cup \left[ 1,2 \right]
  • (-2,-1)\cup (1,2)
Let f (x) = \sqrt {2 - x - x^2} and g(x) = cos x. Which of the following statements are true?
(I) Domain of f((g(x))^2) = Domain of f(g(x))
(II) Domain of f(g(x)) + g(f(x)) = Domain of g(f(x))
(III) Domain of f(g(x)) = Domain of g(f(x))
(IV) Domain of g((f(x))^3) = Domain of f(g(x))
  • Only (I)
  • Only (I) and (II)
  • Only (III) and (IV)
  • Only (I) and (IV)
If f:R\rightarrow R, g:R \rightarrow R be two functions given by f(x)=2x-3 and g(x)=x^3+5, then (fog)^{-1}(x) is equal to
  • \begin{pmatrix}\dfrac{x+7}{2}\end{pmatrix} ^{\dfrac{1}{3}}
  • \begin{pmatrix}\dfrac{x-7}{2}\end{pmatrix} ^{\dfrac{1}{3}}
  • \begin{pmatrix}x-\dfrac{7}{2}\end{pmatrix} ^{\dfrac{1}{3}}
  • \begin{pmatrix}x+\dfrac{7}{2}\end{pmatrix} ^{\dfrac{1}{3}}
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers