Functions Test ...

The domain of $$f(x)=\displaystyle \frac{1}{[x]-x}$$ is

lf $${f}\left({x}\right)=\sin^{2}{x}+\sin^{2}\left({x}+\displaystyle \dfrac{\pi}{3}\right)+ \cos x \cos \left({x}+\displaystyle \dfrac{\pi}{3}\right)$$ and $${g}\left(\displaystyle\dfrac{5}{4}\right)=1$$, $$g\left(1\right) = 0 $$ then $$\left({g}{o}{f}\right)\left({x}\right)=$$

If $$ f : R \rightarrow R$$ is defined by $$f(x)=2x-2,$$  then $$(f\circ f) (x) + 2 =$$

If $$f(x) =\displaystyle \frac{x}{\sqrt{1-x^2}}, g(x)=\frac{x}{\sqrt{1+x^2}}$$ then $$(f\circ g)(x) =$$

If $$f(x)=\log  x,  g(x) = x^3$$ then $$f[g(a)]+f[g(b)]= $$

If $$f:R \rightarrow R$$ and $$g : R \rightarrow R$$ are defined by $$f(x)=2x+3$$ and $$g(x)=x^2+7$$, then the values of $$x$$ such that $$g(f(x)) =8$$ are:

If $$f : R \rightarrow R$$ and $$g :R \rightarrow R$$ are defined by $$f(x) = x -[x]$$ and $$g(x) = [x]$$ for $$x \in R$$, where $$[x]$$ is the greatest integer not exceeding $$x$$, then for every $$x \in R, f(g(x)) =$$

If $$y=f(x) = \dfrac{2x-1}{x-2}$$, then $$f(y)=$$

Find the domain of $$ e^x$$.

A mapping function $$f:X\rightarrow Y$$ is one-one, if