Let $f(x) = \left\{ {\begin{array}{*{20}{c}}
{\,{x^3} - {x^2} + 10x - 5\,\,,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \le 1\,\,\,\,\,\,\,\,\,\,\,\,}\\
{ - 2x + {{\log }_2}({b^2} - 2),\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, > 1\,\,\,\,\,\,\,\,\,\,\,\,}
\end{array}} \right.$ the set of values of $b$ for which $f(x)$ has greatest value at $x = 1$ is given by 

If $y = f(x) = \frac{{ax + b}}{{cx - a}}$, then $x$ is equal to

Range of the function $f(x) = {\sin ^2}({x^4}) + {\cos ^2}({x^4})$ is

Let $f(x) = (1 + {b^2}){x^2} + 2bx + 1$ and $m(b)$ the minimum value of $f(x)$ for a given $b$. As $b$ varies, the range of $m(b)$ is

The period of the function $f (x) =$$\frac{{|\sin x| + |\cos x|}}{{|\sin x - \cos x|}}$  is

Let $f:(1,3) \rightarrow \mathrm{R}$ be a function defined by

$f(\mathrm{x})=\frac{\mathrm{x}[\mathrm{x}]}{1+\mathrm{x}^{2}},$ where $[\mathrm{x}]$ denotes the greatest

integer $\leq \mathrm{x} .$ Then the range of $f$ is