The range of the polynomial $P(x)=4 x^3-3 x$ as $x$ varies over the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is
$[-1,1]$
$(-1,1]$
$(-1,1)$
$\left(-\frac{1}{2}, \frac{1}{2}\right)$
If $f(x + ay,\;x - ay) = axy$, then $f(x,\;y)$ is equal to
The domain of ${\sin ^{ - 1}}({\log _3}x)$ is
The sentence, What is your Name ? is
Show that the function $f: R \rightarrow R$ defined as $f(x)=x^{2},$ is neither one-one nor onto.
Let $f: R \rightarrow R$ be a function defined $f(x)=\frac{2 e^{2 x}}{e^{2 x}+\varepsilon}$. Then $f\left(\frac{1}{100}\right)+f\left(\frac{2}{100}\right)+f\left(\frac{3}{100}\right)+\ldots .+f\left(\frac{99}{100}\right)$ is equal to