The range of the function $f(x){ = ^{7 - x}}{\kern 1pt} {P_{x - 3}}$ is
$\{1, 2, 3, 4, 5\}$
$\{1, 2, 3, 4, 5, 6\}$
$\{1, 2, 3, 4\}$
$\{1, 2, 3\}$
The domain of ${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {\frac{x}{3}} \right)} \right]$ is
Let $f :R \to R$ be defined by $f(x)\,\, = \,\,\frac{x}{{1 + {x^2}}},\,x\, \in \,R.$ Then the range of $f$ is
The function $f(x) = \frac{{{{\sec }^{ - 1}}x}}{{\sqrt {x - [x]} }},$ where $[.]$ denotes the greatest integer less than or equal to $x$ is defined for all $x$ belonging to
Let $f(x)$ be a non-constant polynomial with real coefficients such that $f\left(\frac{1}{2}\right)=100$ and $f(x) \leq 100$ for all real $x$. Which of the following statements is NOT necessarily true?