9000010503
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x}\cdot \root{}\of{x}
\]
\(\root{10}\of{x^{7}}\)
\(\root{10}\of{x}\)
\(\root{5}\of{x^{2}}\)
\(\root{10}\of{x^{2}}\)
B
9000013502
Level:
B
Simplify the expression \(0.5^{\frac{6}
{7} }\cdot 0.5^{-\frac{5}
{14} }\)
and write the result using a root.
\(\sqrt{0.5}\)
\(\root{7}\of{0.5}\)
\(\root{14}\of{0.5^{11}}\)
\(\root{14}\of{0.5}\)
9000010506
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{}\of{x}\cdot \root{3}\of{x}
\]
\(x\root{6}\of{x^{5}}\)
\(\root{6}\of{x^{3}}\)
\(\root{}\of{x}\)
\(x^{5}\root{6}\of{x^{5}}\)
9000010510
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x} : \root{6}\of{x}
\]
\(\root{6}\of{x}\)
\(\root{}\of{x}\)
\(\root{3}\of{x^{2}}\)
\(x\)
9000013501
Level:
B
Write the expression \(2^{\frac{3}
{4} }\)
in an equivalent form which does not contain a rational exponent.
\(\root{4}\of{2^{3}}\)
\(\root{4}\of{2}\)
\(\root{3}\of{2^{4}}\)
\(\root{4}\of{3^{2}}\)
9000013504
Level:
B
Simplify \(\sqrt{\root{4}\of{25}}\).
\(\root{4}\of{5}\)
\(\root{8}\of{5}\)
\(\root{4}\of{25}\)
\(\sqrt{5}\)
9000013507
Level:
B
Simplify \(\root{4}\of{16\cdot 81}\).
\(6\)
\(36\)
\(\sqrt{6}\)
\(\root{4}\of{6}\)
9000007602
Level:
B
Find the domain of the function \(f(x) = 2 - \frac{3}
{x-2}\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{ - 2;2\}\)
\(\mathbb{R}\setminus \{ - 3\}\)
\(\mathbb{R}\)
9000007702
Level:
B
Identify a correct statement which concerns the function
\(f(x) = \frac{1}
{-x+2}\).
None of the statements above is true.
The function \(f\)
is an increasing function.
The function \(f\)
is bounded below.
The function \(f\)
has a maximum at \(x = 2\).
The function \(f\)
is decreasing on \((2;\infty )\).
9000007709
Level:
B
Identify a correct statement which concerns the function
\(f(x) = -\frac{5}
{x} - 3\).
None of the statements above is true.
The function \(f\)
is bounded above.
The function \(f\)
is an even function.
The function \(f\) is a
decreasing function on \((0;\infty )\).
The function \(f\)
is an odd function.