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