If the domain of the function $f(x) = x^2 - 6x + 7$ is $(-\infty, \infty)$,then the range of the function is

Let $A = \{-4, -2, -1, 0, 3, 5\}$ and $f: A \rightarrow R$ be defined by $f(x) = \begin{cases} 3x - 1 & \text{for } x > 3 \\ x^2 + 1 & \text{for } -3 \leq x \leq 3 \\ 2x - 3 & \text{for } x < -3 \end{cases}$. Then the range of $f$ is

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$, where $[y]$ denotes the greatest integer not exceeding $y$, then $\{f(x) : |x| < 71\}$ is equal to

Let $D$ be the domain of the function $f(x) = \sin^{-1} \left(\log_{3x} \left(\frac{6+2 \log_3 x}{-5x}\right)\right)$. If the range of the function $g: D \rightarrow R$ defined by $g(x) = x - [x]$ (where $[x]$ is the greatest integer function) is $(\alpha, \beta)$,then $\alpha^2 + \frac{5}{\beta}$ is equal to

If $f:R \to S$ defined by $f(x) = \sin x - \sqrt{3} \cos x + 1$ is onto,then the interval of $S$ is

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