The range of the real valued function $f(x) = \sqrt{\frac{x^2+2x+8}{x^2+2x+4}}$ is

Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of $g(x) = \log_2\left(2-6\log_{27}(2x+5)\right)$ be $(\gamma, \delta)$. Then $|7(\alpha+\beta)+4(\gamma+\delta)|$ is equal to . . . . . . .

The domain of the real-valued function $f(x) = \frac{\sqrt{|x|-x}}{\sqrt{x-[x]}}$ is

If $f:[2,3] \rightarrow R$ is defined by $f(x)=x^3+3x-2$,then the range of $f(x)$ is contained in the interval

If $[x]^2-5[x]+6=0$,where $[x]$ denotes the greatest integer function,then

Find the domain and the range of the real function $f$ defined by $f(x) = |x - 1|$.