Question Text
Question 1 :
Which of the following functions from $Z$ to itself are bijections?
Question 2 :
If $f:R\rightarrow \left [\dfrac {\pi}{6}, \dfrac {\pi}{2}\right ), f(x)=\sin^{-1}\left (\dfrac {x^2-a}{x^2+1}\right )$ is a onto function, then set of values of $a$ is
Question 3 :
Consider the functions<br>$\displaystyle f: X\rightarrow Y$ and$\displaystyle g: Y\rightarrow Z$<br>then which of the following is/are incorrect?
Question 6 :
Let $R$ a relation on the set $N$ be defined by $\left\{ \left( x,y \right) |x,y\in N,2x+y=41 \right\}$. Then $R$ is
Question 7 :
The function $f:\left[ -\dfrac {1}{2},\dfrac {1}{2} \right] \rightarrow \left[ -\dfrac {\pi }{2},\dfrac {\pi }{2} \right] $ defined by $f(x)=\sin ^{ -1 }{ \left( 3x-4{ x }^{ 3 } \right)  } $ is
Question 8 :
If $f:A\rightarrow B$ given by ${ 3 }^{ f(x) }+{ 2 }^{ -x }=4$ is a bijection, then
Question 9 :
Let $f:R\rightarrow R$ be a function defined by $f(x)=\cfrac { { e }^{ \left| x \right|  }-{ e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } $, then