Mathematics - Functions

Question - 1

If \(f(x)=\frac { x-1 }{ x+1 } \)  , then \(f\left( -\frac { 1 }{ x } \right) \) is equal to 

  • A \(-\frac { 1 }{ f(x) } \)
  • B \(\frac { 1 }{ f(x) } \)
  • C f(x)
  • D -f(x)

Question - 2

The range of f(x)=1+3cos2x is equal to 

  • A [3,2]
  • B [4,2]
  • C [-2,4]
  • D None of these

Question - 3

If f(x) =ax+b, where a and b are integers, f(-1)=-5 and f(3)=3, then a and b are 

  • A a=-3, b=-1
  • B a=2, b=-3
  • C a=0, b=2
  • D a=2, b=3

Question - 4

The range of \(f(x)=\frac { 1 }{ 1-2cosx } \) is equal to 

  • A \(\left[ \frac { 1 }{ 3 } ,1 \right] \)
  • B \(\left[ -1,\frac { 1 }{ 3 } \right] \)
  • C \((-\infty ,-1]\cup [\frac { 1 }{ 3 } ,\infty )\)
  • D \(\left[ -\frac { 1 }{ 3 } ,1 \right] \)

Question - 5

Let \(f:R\rightarrow R\)  be defined as f(x)=3x, then which of the following option is correct? 

  • A f is one-one onto
  • B f is many-one onto
  • C f is one-one but not onto
  • D f is neither one-one nor onto

Question - 6

Let A={1,2,3}, B={4,5,6,7} and f={(1,4),(2,5),(3,6)} be a function from A to B. Then, f is 

  • A one-one 
  • B onto
  • C neither one-one nor onto  
  • D many -one onto

Question - 7

If \(f:R\rightarrow R\) is given by  \(f(x)=\begin{cases} -1,\quad when\quad x\quad is\quad rational \\ 1,\quad when\quad x\quad is\quad irrational \end{cases}\)  \(\left( fof \right) \left( 1-\sqrt { 3 } \right) \) is equal to 

  • A 1
  • B -1
  • C \(\sqrt { 3 } \)
  • D 0

Question - 8

If \(f(x)=\frac { sinx }{ sin\left( \frac { x }{ n } \right) } for\quad n\epsilon Z\) , then value of n, if its period is equal to \(4\pi \) , is 

  • A 2
  • B 13
  • C 4
  • D 5

Question - 9

The domain of the function f denoted by \(f(x)=\sqrt { 4-x } +\frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \) is equal to 

  • A \((-\infty, -1) \cup[1, 4)\)
  • B \((-\infty ,-1)\cup (1,4]\)
  • C \((-\infty ,-1]\cup [1,4]\)
  • D \((-\infty ,-1)\cup (1,4]\)

Question - 10

If \(f:R\rightarrow R\) is given by f(x)=(3-x3)1/3, then fof(x) is equal to 

  • A X1/3
  • B X3
  • C X
  • D 3-X2
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