9000004901
Level:
C
Solve the following inequality.
\[
\log _{0.3}x\geq \log _{0.3}5
\]
\(x\in (0;5] \)
\(x\in (0;\infty )\)
\(x\in (-\infty ;5] \)
\(x\in [ 5;\infty )\)
C
9000003607
Level:
C
The function \(f(x) = \left (\frac{1}
{3}\right )^{x}\)
is graphed in the picture. Identify a possible analytic expression for the function
\(g\).
\(y = 3^{|x|}- 1\)
\(y = \left |\left (\frac{1}
{3}\right )^{x} - 1\right |\)
\(y = \left (\frac{1}
{3}\right )^{|x|}- 1\)
\(y = \left (\frac{1}
{3}\right )^{|x-1|}\)
\(y = \left |3^{x} - 1\right |\)
\(y = 3^{|x-1|}\)
9000003609
Level:
C
Solve the following inequality.
\[
\left (\frac{3}
{4}\right )^{x^{2}-2x
}\leq \frac{4^{x-6}}
{3^{x-6}}
\]
\(x\in (-\infty ;-2] \cup [ 3;\infty )\)
\(x\in \mathbb{R}\setminus \{ - 2;3\}\)
\(x\in \mathbb{R}\setminus \{ - 3;2\}\)
\(x\in [ - 2;3] \)
9000003709
Level:
C
Solve the following inequality.
\[
\left (\frac{2}
{3}\right )^{2-3x} < \frac{2^{x+1}}
{3^{x+1}}
\]
\(\left (-\infty ; \frac{1}
{4}\right )\)
\(\left (-\frac{1}
{4};\infty \right )\)
\((-\infty ;4)\)
\(\left (\frac{1}
{4};\infty \right )\)
\((4;\infty )\)
\(\left (-\infty ;-\frac{1}
{4}\right )\)
9000003809
Level:
C
Find the solution set of the following inequality.
\[
\log _{0.5}(x^{2} - 2x) >\log _{
0.5}3
\]
\((-1;0)\cup (2;3)\)
\((-\infty ;0)\cup (2;\infty )\)
\((0;2)\)
\((-\infty ;-1)\cup (0;2)\cup (3;\infty )\)
\((-\infty ;-1)\cup (3;\infty )\)
\((-1;3)\)
9000002908
Level:
C
Find the intervals where the function
\(f(x) = \left |1 + \frac{1}
{x}\right |\) is an increasing
function. The function \(f\)
is graphed in the picture.
\([ - 1;0)\)
\((-\infty ;1] \)
\((-\infty ;0)\)
\((0;\infty )\)
9100004009
Level:
C
Identify a possible graph of the function
\(g(x) ={\Bigl | |x - 2|- 1\Bigr |}\).
9100004010
Level:
C
Identify a possible graph of the function
\(g\colon y ={\Bigl | |x - 1|- 1\Bigr |} - 1\).
9100026110
Level:
C
Identify the picture which shows the solution of the following equation.
\[
\frac{1}
{x - 1} = x
\]
The solution set is drawn in a red color.
9100033309
Level:
C
Identify the picture which shows the solution of the following inequality.
\[
\frac{1}
{x} > 1
\] The solution set is drawn in a red color.
