Functions Test ...

$\displaystyle f\left ( x \right )= \log \left | 4-x^{2} \right |$ then domain of $x$ is

The domain of $\displaystyle \frac{1}{\log _{10}\left ( 1-x \right )}+\sqrt{\left ( x+2 \right )}$ is

$\displaystyle f\left ( x \right )=\dfrac1{\left ( \left | x \right |-x \right )^{1/2}}$. Then the domain of the function is

The domain of $\displaystyle f\left ( x \right )= \sqrt{\log \left ( \dfrac{ 5x-x^{2}}6 \right )}$ is

Determine domain of $\displaystyle \frac{\sqrt{4-x^{2}}}{\sin ^{-1}\left ( 2-x \right )}$

The domain of $\displaystyle \log \left [ 1-\log _{10}\left ( x^{2}-5x+16 \right ) \right ]$ is

If $\displaystyle f\left ( x \right )=\frac{ax+b}{cx+d}$ and $\displaystyle \left ( fof \right )x=x,$ then d=?

The domain of the function $\displaystyle \sqrt{\left \{ \frac{\log _{0.3}\left | x-2 \right |}{\left | x \right |} \right \}}$ is

The total number of injective mappings from a set with $m$ elements to a set with $n$ elements,$\displaystyle m\leq n,$ is