Domain of function $f(x) = {\sin ^{ - 1}}5x$ is
$\left( { - \frac{1}{5},\;\frac{1}{5}} \right)$
$\left[ { - \frac{1}{5},\;\frac{1}{5}} \right]$
$R$
$\left( {0,\;\frac{1}{5}} \right)$
The number of one-one function $f :\{ a , b , c , d \} \rightarrow$ $\{0,1,2, \ldots ., 10\}$ such that $2 f(a)-f(b)+3 f(c)+$ $f ( d )=0$ is
The domain of the function $f(x)=\frac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $x$ )
Let a function $f : R \rightarrow R$ is defined such that $3f(2x^2 -3x + 5) + 2f(3x^2 -2x + 4) = x^2 -7x + 9\ \ \ \forall x \in R$, then the value of $f(5)$ is-
Domain of the function $f(x) = {\sin ^{ - 1}}(1 + 3x + 2{x^2})$ is
If $f(x)$ be a polynomial function satisfying $f(x).f (\frac{1}{x}) = f(x) + f (\frac{1}{x})$ and $f(4) = 65$ then value of $f(6)$ is