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.
\[ \left(x^6+2\right)\left(x^2+1\right) > 0 \]
\( \mathbb{R} \)
\(( 1,\infty) \)
\(( -1,\infty) \)
\(( 0,\infty) \)