Functions Test ...

The domain of the function $$\displaystyle f(x)={}^{16-x}C_{2x-1}+{}^{20-3x}P_{4x-5},$$ where the symbols have their usual meanings, is the set:

The largest set of real values of $$x$$ for which $$\displaystyle f(x)=\sqrt{(x+2)(5-x)}-\frac{1}{\sqrt{x^{2}-4}}$$ is a real function is

The domain of $$\displaystyle f(x)=\frac{1}{\sqrt{|\cos\:x|+\cos\:x}}$$ is 

If $$y$$ is a function of $$x$$ defined by $$\displaystyle a^{x+y}=a^{x}+a^{y}$$ where $$a$$ is a real constant $$\displaystyle (a>1)$$ then the domain of $$y(x)$$ is 

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

If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ are given by $$f(x)=|x|$$ and $$g(x)=[x]$$ for each $$x\in R,$$ then $$\left\{ x\in R:g\left( f\left( x \right) \right) \le f\left( g\left( x \right) \right)  \right\} =$$

Let $$f$$ and $$g$$ be increasing and decreasing functions respectively from $$\displaystyle \left ( 0,\infty  \right )$$ to $$\left ( 0,\infty  \right )$$ and let $$h\left ( x \right )=f\left [ g\left ( x \right ) \right ]$$. If $$h\left ( 0 \right )=0$$ then $$ h\left ( x \right )-h\left ( 1 \right )$$ is

The domain of $$\displaystyle \cos ^{-1}\left ( \frac{2-\left | x \right |}{4} \right )+\left [ \log \left ( 3-x \right ) \right ]^{-1}$$ is

Let $$\displaystyle f\left ( x \right )=\frac{ax^{2}+2x+1}{2x^{2}-2x+1}$$, the value of $$a$$ for which $$\displaystyle f:R\rightarrow \left [ -1,2 \right ]$$ is onto , is

The value of $$x$$ satisfying the equation $$\displaystyle \left | x-1 \right |^{\log_{3}x^{2}-2\log_{9}x}= (x-1)^7$$ is