1003187403
Level:
C
How many solutions does the equation \( \left| |2x+6|-8\right|=4 \) have?
\( 4 \)
\( 2 \)
\( 0 \)
\( 6 \)
C
1003187401
Level:
C
Give the solution set of the equation \( \left| |x-1|-|3-x| \right|=2 \).
\( (-\infty;1]\cup[3;+\infty) \)
\( (-\infty;1)\cup(3;+\infty) \)
\( \mathbb{R} \)
\( (1;3) \)
1003170904
Level:
C
Find the solution set of the following inequality.
\[ \frac{\log x-1}{2+\log x}\geq1 \]
\( \left(0;\frac1{100}\right) \)
\( \left(0;\frac1{100}\right] \)
\( \left(-\infty;\frac1{100}\right) \)
\( \left(-\infty;\frac1{100}\right] \)
1003170903
Level:
C
Find the solution set of the following inequality.
\[ \log_2^2(x-2)< \log_2(x-2) \]
\( (3;4) \)
\( (0;1) \)
\( (-\infty;4) \)
\( (-\infty;1) \)
1003170902
Level:
C
Find the solution set of the following inequality.
\[ \log_{0.1}\frac{2-x}{x+1}>0 \]
\( \left(\frac12;2\right) \)
\( (-\infty;-1)\cup\left(\frac12;\infty\right) \)
\( \left(-1;\frac12 \right) \)
\( (-1;2) \)
1003170901
Level:
C
Find the solution set of the following inequality.
\[ \log_3\frac{2x-2}{x+3}\leq 0 \]
\( (1;5] \)
\( (-3;5] \)
\( [-3;5] \)
\( [-3;1] \)
1003134510
Level:
C
Complete the following sentence to obtain a true statement. The number \( \left( \sqrt3 \right)^{\sqrt2^{\sqrt[3]{64}}} \) is ...
a rational number less than \( 10 \).
an irrational number less than \( 10 \).
an integer greater than \( 10 \).
a rational number greater than \( 10 \).
1003134508
Level:
C
The number \( \left(\sqrt2-1\right)^6 \) is equal to:
\( 99-70\sqrt2 \)
\( 5\sqrt2 - 7 \)
\( 49-35\sqrt2 \)
\( 34-24\sqrt2 \)
1103120010
Level:
C
Let \( f(x)=(x+a)^2+b \) and \( g(x)=(x+a-2)^2+b+3 \), where \( a \), \( b\in\mathbb{R} \). In which of the next four given pictures are the graphs of both functions \( f \) and \( g \)?
1103120009
Level:
C
In the picture there are two parabolas. One parabola can be mapped onto the other by shifting. These parabolas are graphs of the quadratic functions
\[ f(x)=-(x-a)^2+b\ \text{ and }\ g(x)=-(x-c)^2+d, \]
where \( a \), \( b \), \( c \), \( d\in\mathbb{R} \).
Following statements describe the relations between the pairs of the coefficients \( a \), \( b \), \( c \) and \( d \). Choose the true statement.
\( a=c-1\wedge b=d+4 \)
\( a=c+1\wedge b=d-4 \)
\( a=c-4\wedge b=d+1 \)
\( a=c+4\wedge b=d-1 \)