### 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