B

2010011005

Level: 
B
If \( a \), \( b \), \( c\in(0;\infty) \) then the expression \( \log_2a+3 \log_2 b-\frac12 \log_2⁡c \) is equivalent to:
\( \log_2\frac{ab^3}{\sqrt{c}} \)
\( \log_2\frac{3ab}{\frac12 c} \)
\( \log_2 \left({ab^3}{c}^{\frac12} \right)\)
\( \log_2 \left(-\frac32 abc\right) \)

2010009901

Level: 
B
Find the domain \(\mathrm{Dom}(f)\) and range \(\mathop{\mathrm{Ran}}(f)\) of the function \(f(x) = \frac{x-3} {x+1}\).
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;-1)\cup (-1;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;1)\cup (1;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;-1)\cup (-1;\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;3)\cup (3;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;-1)\cup (-1;\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;-3)\cup (-3;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty ) \end{align*}