Functions Test ...

Domain of the function $$\displaystyle \frac{1}{\sqrt{^{10}C_{x-1}-3^{10}C_{x}}}$$ is given by

Find all posible values of $$x$$ satisfying $$\displaystyle \dfrac{\left [ x \right ]}{\left [ x-2 \right ]}-\dfrac{\left [ x-2 \right ]}{\left [ x \right ]}=\dfrac{8\left \{ x \right \}+12}{\left [ x-2 \right ]\left [ x \right ]}$$ (where $$[\cdot]$$ denotes the greatest integer function and $$\{\cdot\}$$ is fractional part).

Let $$f(x)=\ln x$$  and  $$g(x)\, =\, \left (\displaystyle \frac{x^{4}\, -\, x^{3}\, +\, 3x^{2}\, -\, 2x\, +\, 2}{2x^{2}\, -\, 2x\, +\, 3 )}\right )$$. The domain of $$f(g(x))$$ is

The domain of the function $$ f(x)=\sqrt{\log _{\sin x+\cos x}(\left| \cos x\right|+\cos x)},0\leq x \leq \pi$$ is

Let $$f(x) = \begin{cases} 1+x, & 0\leq x\leq 2 \\ 3-x, & 2<x\leq 3 \end{cases}$$, then find $$(fof)(x)$$

Given two functions $$f(x)$$ and $$g(x)$$ such that $$f(x) = \sin (arctan x), g(x) =\tan (arc\sin x)$$, and $$0\leq x < \dfrac {\pi}{2}$$. The value of the composite function $$f\left (g\left (\dfrac {\pi}{10}\right )\right ) $$ is:

If $$f(x) = x^{2} + x$$ and $$g(x) = \sqrt {x}$$, then the value of $$f(g(3))$$ is

If $$f(x)=2x^3$$ and $$g(x)=3x$$, calculate the value of $$g(f(-2))-f(g(2))$$.

$$f(x)\, =\, -1\, + |x\, -\, 2|, \, 0\, \leq\, x\, \leq\, 4$$
$$g(x)\, =\, 2\, -\, |x|,\, -1\, \leq\, x\, \leq\, 3$$
Which of the following is true