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CBSE Questions for Class 12 Commerce Maths Relations And Functions Quiz 6 - MCQExams.com

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
Find g(x), if f(x)=7x+12 and f(g(x)=21x2+40
  • 21x2+28
  • 21x2
  • 7x2+4
  • 3x2+28
  • 3x2+4
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
Extraction of a cube root of a given number is
  • binary operation
  • relation
  • unary operation
  • relation in some set
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))
* is a binary operation on Z such that:
a * b = a + b + ab.
The solution of (3* 4) *x = -1 is

  • 1
  • -1
  • 4
  • 3
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 a*b = |a-b| then 6*8 will be
  • -2
  • 14
  • 2
  • Cannot be determined
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
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}
If f(x) = 2x - 6, then f^{-1}(x) is
  • 6 - 2x
  • \dfrac {1}{2}x - 6
  • \dfrac {1}{2}x - 3
  • \dfrac {1}{2}x + 3
  • \dfrac {1}{2} x + 6
If f(x) = 4/\sqrt [3]{x + 1}, what is f^{-1}(7)?
  • -7
  • 8
  • -\dfrac{279}{343}
  • 1.75
  • 7.2
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
If the operation \oplus is defined by a\oplus b = a^{2} + b^{2} for all real numbers 'a' and 'b', the (2\oplus 3)\oplus 4 =  
  • 120
  • 175
  • 129
  • 185
  • 312
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
If f : IR \rightarrow IR is defined by f(x) = 2x + 3, then f^{-1}(x)
  • Is given by \dfrac{x-3}{2}
  • Is given by \dfrac{1}{2x + 3}
  • Does not exist because 'f' is not injective
  • Does not exist because 'f' is not surjective
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
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
In the set of integers under the operation \ast defined by a\ast b=a+b-1, the identity element is:
  • 0
  • 1
  • a
  • b
Which of the following is not a binary operation on R?
  • a \times b = ab
  • a \times b = a - b
  • a \times b = \sqrt{ab}
  • a \times b = \sqrt{a^2 + b^2}
If N is a set of natural numbers, then under binary operation a\cdot b = a + b, (N, .) is
  • Quasi-group
  • Semi-group
  • Monoid
  • Group
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}
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
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.
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
On the set Z, of all integers \ast is defined by a\ast b = a + b - 5. If 2\ast (x\ast 3) = 5 then x =
  • 0
  • 3
  • 5
  • 10
If f(x) = 8x^3, g(x) = x^{1/3}, then fog (x) is
  • 8^3x
  • (8x)^{1/3}
  • 8x^3
  • 8x
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)))))
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}}
If f : R \rightarrow R is defined by f(x) = x^{3} then f^{-1}(8) =
  • \left \{2\right \}
  • \left \{2, 2\omega, 2\omega^{2}\right \}
  • \left \{2, -2\right \}
  • \left \{2, 2\omega\right \}
Let A=\left\{ x\in R|x\ge 0 \right\} . A function f:A\rightarrow A is defined by f(x)={ x }^{ 2 }. Which one of the following is correct?
  • The function does not have inverse
  • f is its own inverse
  • The function has an inverse but f is not its own inverse
  • None of the above
If f:[0, \infty)\to [0,\infty) and f(x) = \dfrac{x}{1+x}, then f is 
  • One-one and onto
  • One-one but not onto
  • Onto but not one-one
  • Neither one-one nor onto
If \ast is the operation defined by a\ast b={ a }^{ b } for a,b\in N, then \left( 2\ast 3 \right) \ast 2 is equal to
  • 81
  • 512
  • 216
  • 64
  • 243
The function f:A\rightarrow B given by f(x) = x ,x\in A, is one to one but not onto. Then;
  • B\subset A
  • A=B
  • A'\subset B'\quad
  • A\subset B
  • A'\cap B'=\phi
If fog = |\sin x| and gof = \sin^{2}\sqrt {x}, then f(x) and g(x) are
  • f(x) = \sqrt {\sin x}, g(x) = x^{2}
  • f(x) = |x|, g(x) = \sin x
  • f(x) = \sqrt {x}, g(x) = \sin^{2}x
  • f(x) = \sin \sqrt {x}, g(x) = x^{2}
Let f(x) = |x - 2|, 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
The value of \alpha (\neq 0) for which the function f(x) = 1 + \alpha x is the inverse of itself is
  • -2
  • 2
  • -1
  • 1
If A = \left \{ 1 , 3 , 5 , 7 \right \} and B = \left \{ 1 , 2 , 3, 4 , 5 , 6 , 7 , 8 \right \} 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)={ x }^{ 2 }-1, then \left( f\circ g \right) ({ x }^{ 2 }-1) is equal to
  • 3{ x }^{ 4 }-3x+5
  • 3{ x }^{ 4 }-6{ x }^{ 2 }+5
  • 6{ x }^{ 4 }+3{ x }^{ 2 }+5
  • 6{ x }^{ 4 }-6x+5
  • 3{ x }^{ 2 }+6x+4
If \ast is defined by a\ast b = a - b^{2} and \oplus is defined by a\oplus b = a^{2} + b, where a and b are integers, then (3\oplus 4)\ast 5 is equal to
  • 164
  • 38
  • -12
  • -28
  • 144
If g(x)=1+\sqrt{x} and f\{g(x)\}=3+2\sqrt{x}+x, then f(x) is equal to
  • 1+2x^2
  • 2+x^2
  • 1+x
  • 2+x
Let f(x)=\cot ^{ -1 }{ \left( \cfrac { 1-{ x }^{ 2 } }{ 2x }  \right)  } +\cot ^{ -1 }{ \left( \cfrac { 1-3{ x }^{ 2 } }{ 3x-{ x }^{ 3 } }  \right)  } -\cot ^{ -1 }{ \left( \cfrac { 1-6{ x }^{ 2 }+{ x }^{ 4 } }{ 4x-4{ x }^{ 3 } }  \right)  } , the F'(x) equals
  • \cfrac { -1 }{ \sqrt { 1-{ x }^{ 2 } } }
  • \cfrac { -1 }{ 1+{ x }^{ 2 } }
  • \cfrac { 1 }{ 1+{ x }^{ 2 } }
  • \cfrac { 1 }{ \sqrt { 1-{ x }^{ 2 } } }
If f(x)=\left| x \right| ,x\in R, then
  • f(x)=\left( f\times f \right) \left( x \right)
  • f(x)=x
  • f(x)=\left( f\times f \right) \left( x^2 \right)
  • f(x)=\left( f\circ f \right) \left( x \right)
If g(x)={ x }^{ 2 }+x-2 and \cfrac { 1 }{ 2 } (g\circ f)(x)=2{ x }^{ 2 }-5x+2, then f(x) is
  • 2x-3
  • 2x+3
  • 2{ x }^{ 2 }+3x+1
  • 2{ x }^{ 2 }+3x-1
If (ax^2 + bx + c)y +a'x^2+b'x+c=0, then the condition that x may be a rational function of y is
  • (ac'-a'c)^2=(ab'-a'b)(bc'-b'c)
  • (ab'-a'b)^2=(ab'-a' c)(bc'-b'c)
  • (bc'-b'c)^2=(ab'-a'b)(ac'-a'c)
  • None of these
If f(x)=\sin ^{ 2 }{ x } +\sin ^{ 2 }{ \left( x+\cfrac { \pi  }{ 3 }  \right)  } +\cos { x } \cos { \left( x+\cfrac { \pi  }{ 3 }  \right)  } and g\left( \cfrac { 5 }{ 4 }  \right) =1, then g\circ f(x) is equal to
  • 0
  • 1
  • \sin { { 1 }^{ o } }
  • None of these
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers