9000010505
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x^{3}} : \root{3}\of{x}
\]
\(\root{15}\of{x^{4}}\)
\(\root{5}\of{x}\)
\(\root{3}\of{x^{2}}\)
\(\root{5}\of{x^{2}}\)
B
9000010508
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{2}}\cdot \root{5}\of{x^{4}}
\]
\(\root{15}\of{x^{22}}\)
\(\root{15}\of{x^{6}}\)
\(\root{15}\of{x^{8}}\)
\(x^{3}\root{15}\of{x}\)
9000007507
Level:
B
The graph of the function
\[
f(x) = \frac{2x - 4}
{3x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = \left [-\frac{2}
{3}; \frac{2}
{3}\right ]\)
\(S = \left [-\frac{3}
{2}; \frac{2}
{3}\right ]\)
\(S = \left [\frac{2}
{3};-\frac{3}
{2}\right ]\)
\(S = \left [-\frac{2}
{3};-\frac{2}
{3}\right ]\)
\(S = \left [\frac{3}
{2}; \frac{3}
{2}\right ]\)
9000007508
Level:
B
The graph of the function
\[
f(x) = \frac{2x + 1}
{x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-2;2]\)
\(S = [2;-2]\)
\(S = [2;2]\)
\(S = [-2;-2]\)
\(S = [-2;3]\)
9000007601
Level:
B
Find the domain of the function \(f(x) = 1 + \frac{3}
{x+2}\).
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{1;2\}\)
\(\mathbb{R}\setminus \{ - 2;1\}\)
\(\mathbb{R}\)
9000007509
Level:
B
The graph of the function
\[
f(x) = \frac{2x + 3}
{2 - x}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [2;-2]\)
\(S = [-2;2]\)
\(S = [2;2]\)
\(S ={\Bigl [ 2; \frac{3}
{2}\Bigr ]}\)
\(S ={\Bigl [ 2;-\frac{3}
{2}\Bigr ]}\)
9000007606
Level:
B
Find the range of the function \(f(x) = 1 + \frac{3}
{x+2}\).
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{ - 2;1\}\)
\([ 0;\infty )\)
\(\mathbb{R}\)
9000007510
Level:
B
The graph of the function
\[
f(x) = \frac{-x + 1}
{1 + 3x}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = \left [-\frac{1}
{3};-\frac{1}
{3}\right ]\)
\(S = \left [\frac{1}
{3}; \frac{1}
{3}\right ]\)
\(S = \left [1;-\frac{1}
{3}\right ]\)
\(S = \left [-1;-\frac{1}
{3}\right ]\)
\(S = \left [-\frac{1}
{3}; \frac{1}
{3}\right ]\)
9000007607
Level:
B
Find the range of the function \(f(x) = 2 - \frac{3}
{x-2}\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{ - 2;3\}\)
\((0;\infty )\)
\(\mathbb{R}\)
9000007707
Level:
B
Identify a correct statement which concerns the function
\(f(x) = 2 -\frac{1}
{x}\).
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 bounded function.
The function \(f\)
is an odd function.