Tag: mathematics and statistics

If $f(x)=\dfrac {1}{x^{2}-17x+66}$ then $f\left(\dfrac {2}{x-2}\right)$ is discontinuous at $x=$

The sum of all values of $x$ for which $f(x)=[3\sin x]$ is discontinous in $[0,\ 2\pi]$ is (where [.] represents greatest integers function)

Consider the function defined on $[0,\ 1]\rightarrow R,\ f(x)=\dfrac {\sin x-x\cos x}{x^{2}}$ if $x\neq 0$ and $f(0)=0$ then the function of $f(x)$. 

The function $f(x)={ sin }^{ -1 }(cosx)$ is :

If $f\left( x \right) =\begin{cases} -1,if\ x<0\ \ 0,if\ x=0\ \ 1,if\ x>0\ \end{cases}$ and $g\left(x\right)=\sin x +\cos x$, then point discontinuity of $(fog)(x)$ in $(0,2\pi)$ are 

$f(x)=\min { \left{ x,{ x }^{ 2 } \right} ,\forall x\epsilon R } $ then $f(x)$ is 

If $f(x)=\dfrac{1}{1-x}$, the number of points of discontinuity of $f\left{f[f(x)]\right}$ is:

Consider  $f ( x ) = \sin x \forall x \in \left[ 0 , \dfrac { \pi } { 2 } \right] ; f ( x ) + f ( \pi - x ) =2 \forall x \in \left( \dfrac { \pi } { 2 } , \pi \right) \text { and } f ( x ) = f ( 2 \pi - x ) \forall x \in ( \pi , 2 \pi ) . \text { If } n , m$ denotes number of points where  $f(x)$  is discontinuous and non derivable respectively in  $[ 0,2 \pi ]$  then value of  $n \div  m$  is

f(x) = $\dfrac{\sin2x + 1}{\sin x - \cos x}$ is discontinuous at $x =$ ____________.

The function $\displaystyle f\left ( x \right )=\frac{\log \left ( 1+ax \right )-\log \left ( 1-bx \right )}{x}$ is not defined at $ x = 0$. The value which should be assigned to $f$ at $x =0$ so that it is continuous there, is