Functions Test ...

The domain of $$f(x)=\sqrt { x-4-2\sqrt { (x-5) }  } -\sqrt { x-4+2\sqrt { (x-5) }  } $$ is 

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

The domain of $$f(x)=\dfrac { 1 }{ \sqrt { \left| \cos x \right| +\cos x}  } $$ is 

The domain of the function $$\sqrt { (\log\ 5x) } $$ is 

The domain of function $$f(x) = \log_{3 + x}(x^{2} -1)$$ is 

The domain of the function $$f(x) = \left [ log_{10} \left ( \frac{5x - x^{2}} {4} \right ) \right]^{1/2}$$ is 

If $$\displaystyle {f}'(x) = g\,(x) $$ and $$\displaystyle {g}'(x) = - f\,(x) $$ for all $$ x $$ and $$ f\,(2) = 4 = {f}'(2) $$ then $$\displaystyle f^{2}\,(19) + g^{2} \,(19) $$ is 

Let $$f(n)$$ denote the number of different ways in which the positive integer $$n$$ can be expressed as the sum of $$1s$$ and $$2s$$. For example, $$f(4) = 5$$, since $$4 = 2 + 2 = 2 + 1 + 1 = 1 + 2 + 1 = 1 + 1 + 2 = 1 + 1 + 1 + 1$$. Note that order of $$1s$$ and $$2s$$ is important.

let $$f(x) = sin^2 x/2 + cos ^2 x/2 $$ and $$g(x) = sec^2 x - tan ^2 x.$$ The two functions are equal over the set

The value of f(0), so that the function
f(x) = $$ \dfrac{2x-sin^{-1}x}{2x+tan^{-1}x} $$ is continuous at each point in its domain, is equal to