2010010008
Level:
B
Choose the set equal to \( \{ x \in \mathbb{N}: |x|< 3 \}\).
\( \{ 1;2\}\)
\( \{ 0;1;2;3\}\)
\( \{ -2;-1;0;1;2\}\)
\( \{ 1;2;3\}\)
B
2010010007
Level:
B
Choose the set equal to \( \{ x \in \mathbb{Z}: |x|< 4 \}\).
\( \{ -3;-2;-1;0;1;2;3\}\)
\( \{ 0;1;2;3\}\)
\( \{ 1;2;3\}\)
\( \{ -1;0;1\}\)
2010010002
Level:
B
Choose the set with all the elements satisfying the given inequality.
\[ |x|>3\]
\( x \in \{-5;-4;4;5\}\)
\( x \in \{0;1;2\}\)
\( x \in \{-5;-4;-3\}\)
\( x \in \{3;4;5\}\)
2010010001
Level:
B
Choose the set with all the elements satisfying the given inequality.
\[|x| < 3\]
\( x \in \{-1;0;2\}\)
\( x \in \{1;2;3\}\)
\( x \in \{-3;-2;-1;0\}\)
\( x \in \{-4;-2;0\}\)
2010009903
Level:
B
Consider the function \(f(x) = \frac{6}
{x-1}-1 \).
Find all \(x\)
such that \(f(x) < 0\).
\(x\in \left (-\infty ;1\right )\cup (7;\infty )\)
\(x\in \left (-\infty ;-7\right )\cup (-1;\infty )\)
\(x\in (7;\infty)\)
\(x\in (-\infty;7)\)
2010009902
Level:
B
Consider the function \(f(x) = \frac{-1}
{x+2}-1 \).
Find all \(x\)
such that \(f(x) > 0\).
\(x\in (-3;-2)\)
\(x\in (-2;3)\)
\(x\in \left (-\infty ;-3\right )\cup (-2;\infty )\)
\(x\in \left (-\infty ;-2\right )\cup (3;\infty )\)
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*}
2010009606
Level:
B
Find the solution set of the inequality.
\[ \left(4-x^2\right)\left(x^3+1\right) > 0 \]
\( (-\infty;-2)\cup(-1;2) \)
\( (-\infty;-2)\)
\( (-\infty;2) \)
\( (-\infty;-1)\cup(0;2) \)
2010009605
Level:
B
Assuming \(x\in \mathbb{R}\),
solve the following algebraic equation.
\[
x^{4} -3x^{2} - 4 = 0
\]
\( \{ -2;2\} \)
\( \{ 2\} \)
\( \{ -2;-1;1;2\} \)
\( \{ -1;2\} \)
2010009604
Level:
B
Find the solution set of the inequality.
\[ \left(x^6+2\right)\left(x^2+1\right) > 0 \]
\( \mathbb{R} \)
\(( 1;\infty) \)
\(( -1;\infty) \)
\(( 0;\infty) \)