If the domain and range of $f(x){ = ^{9 - x}}{C_{x - 1}}$ contains $m$ and $n$ elements respectively, then
$m = n$
$m = n + 1$
$m = n -1$
$m = n + 2$
If domain of function $f(x) = \sqrt {\ln \left( {m\sin x + 4} \right)} $ is $R$ , then number of possible integral values of $m$ is
Let $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of functions $f: A \rightarrow B$ satisfying $f(1)+f(2)=f(4)-1$ is equal to
Let $f :R \to R$ be defined by $f(x)\,\, = \,\,\frac{x}{{1 + {x^2}}},\,x\, \in \,R.$ Then the range of $f$ is
If $f(x) = \cos (\log x)$, then $f(x)f(y) - \frac{1}{2}[f(x/y) + f(xy)] = $