Functions Test ...

Given that, $$x$$ is a real number satisfying $$\dfrac{5x^2-26x+5}{3x^2-10x+3}<0$$, then

If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ are defined by $$f\left( x \right) =\left| x \right| $$ and $$g\left( x \right) =\left[ x-3 \right] $$ for $$x\in R$$, then
$$g\left( f\left( x \right)  \right) :\left\{ -\dfrac { 8 }{ 5 } < x < \dfrac { 8 }{ 5 }  \right\} $$ is equal to

Let $$R$$ be the set of real numbers and the functions $$f: R \rightarrow R$$ and $$g: R\rightarrow R$$ be defined by $$f(x) = x^{2} + 2x - 3$$ and $$g(x) = x + 1$$. Then the value of $$x$$ for which $$f(g(x)) = g(f(x))$$ is

Let $$f:R\rightarrow R$$ be such that $$f$$ is injective and $$f(x)f(y)=f(x+y)$$ for all $$x,y\in R$$, if $$f(x), f(y)$$ and $$f(z)$$ are in GP, then $$x,y$$ and $$z$$ are in

Let Q be the set of all rational numbers in [0, 1] and $$f : [0, 1]\rightarrow [0, 1]$$ be defined by $$f(x)=\begin{cases}x&for&x\in Q\\ 1-x&for&x\notin Q\end{cases}$$
Then the set $$S=\{x\in [0, 1]: (f\, o \, f)(x)=x\}$$ is equal to

If $$f(x)={2}^{100}x+1, g(x)={3}^{100}x+1$$, then the set of real numbers $$x$$ such that $$f\left\{ g(x) \right\} =x$$ is

If $$f(x) =$$ $$\sqrt{x}$$ and $$g(x) =$$ $$\sqrt{x^2+4}$$, calculate the value of $$f(g(2))$$.

If $$f: R\rightarrow R^{+}$$ and $$g: R^{+} \rightarrow R$$ are such that $$g(f(x)) = |\sin x|$$ and $$f(g(x)) = (\sin \sqrt {x})^{2}$$, then a possible choice for f and g is

The domain of the function $$f(x) = \log (1 - x) + \sqrt {x^{2} - 1}$$

If $$h(x)={x}^{3}+x$$ and $$g(x)=2x+3$$, then calculate $$g(h(2))$$.