9000010506
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{}\of{x}\cdot \root{3}\of{x}
\]
\(x\root{6}\of{x^{5}}\)
\(\root{6}\of{x^{3}}\)
\(\root{}\of{x}\)
\(x^{5}\root{6}\of{x^{5}}\)
B
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 \(\root{4}\of{16\cdot 81}\).
\(6\)
\(36\)
\(\sqrt{6}\)
\(\root{4}\of{6}\)
9000010601
Level:
B
Identify a function which has a domain
\([ - 3;1] \).
\(y = \sqrt{-x^{2 } - 2x + 3}\)
\(y = \sqrt{-x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } - 2x + 3}\)
\(y = \sqrt{\frac{x+3}
{x+1}}\)
\(y = \sqrt{\frac{x-1}
{x+3}}\)
9000010603
Level:
B
Identify a function which has a domain
\(\left (-\infty ;-\frac{3}
{2}\right ] \).
\(y = \sqrt{-2x - 3}\)
\(y = \sqrt{3x + 2}\)
\(y = -\sqrt{2 - 3x}\)
\(y = \sqrt{x + \frac{3}
{2}}\)
\(y = \sqrt{x^{2 } - 3x}\)
\(y = \frac{1}
{3x+2}\)
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.
9000007504
Level:
B
The graph of the function
\[
f(x) = \frac{3}
{-2(x + 3)} - 1
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-3;-1]\)
\(S = [3;-1]\)
\(S = [3;1]\)
\(S = \left [\frac{3}
{2};-1\right ]\)
\(S = \left [-\frac{3}
{2};-1\right ]\)
9000007505
Level:
B
The graph of the function
\[
f(x) = \frac{1}
{-x + 3} + 2
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [3;2]\)
\(S = [-3;2]\)
\(S = [1;2]\)
\(S = [2;3]\)
\(S = [3;1]\)