Let $f: R \rightarrow R$ be a function defined by $f(x)=\left\{\begin{array}{l}\frac{\sin \left(x^2\right)}{x} \text { if } x \neq 0 \\ 0 \text { if } x=0\end{array}\right\}$ Then, at $x=0, f$ is

Let $f(x) = \frac{{x\,\, – \,\,1}}{{2\,{x^2}\,\, – \,\,7x\,\, + \,\,5}}$ . Then :

A real valued function $f(x)$ satisfies the function equation $f(x – y) = f(x)f(y) – f(a – x)f(a + y)$ where a is a given constant and $f(0) = 1$, $f(2a – x)$ is equal to

Let $2{\sin ^2}x + 3\sin x – 2 > 0$ and ${x^2} – x – 2 < 0$ ($x$ is measured in radians). Then $x$  lies in the interval

If $f(x) = \frac{1}{{\sqrt {x + 2\sqrt {2x – 4} } }} + \frac{1}{{\sqrt {x – 2\sqrt {2x – 4} } }}$ for $x > 2$, then $f(11) = $