1003187205
Level:
C
Let \( f(x)=\left|3|2x-1|-9\right| \). The number of argument values \( x \) for which \( f(x)=2 \) is:
\( 4 \)
\( 2 \)
\( 3 \)
\( 1 \)
C
1003187204
Level:
C
The solution set of the equation \( \sqrt{x^2-2x+1}-2|x+3|+x+7=0 \) is:
\( \{-7\}\cup[1;+\infty) \)
\( \{-7\}\cup(1;+\infty) \)
\( [1;+\infty) \)
\( (1;+\infty) \)
1003187203
Level:
C
How many solutions does the equation \( \sqrt{x^2-4x+4}=|x| \) have?
\( 1 \)
\( 2 \)
\( 0 \)
\( 3 \)
1003187202
Level:
C
Which of following equalities is true for all real numbers \( x \)?
\( \sqrt{(x-3)^2} = |x-3| \)
\( |-x| = x \)
\( |x-1|=x-1 \)
\( \sqrt{x^2} = x \)
1003187410
Level:
C
How many integers are in the solution set of the given inequalities?
\[ \left|\sqrt{17}-2x\right| \leq 5 \text{ and } \left|2x-\sqrt{17}\right| \leq 5 \]
\( 5 \)
\( 4 \)
\( 6 \)
\( 7 \)
1003187403
Level:
C
How many solutions does the equation \( \left| |2x+6|-8\right|=4 \) have?
\( 4 \)
\( 2 \)
\( 0 \)
\( 6 \)
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.
\[ \log_{0.1}\frac{2-x}{x+1}>0 \]
\( \left(\frac12;2\right) \)
\( (-\infty;-1)\cup\left(\frac12;\infty\right) \)
\( \left(-1;\frac12 \right) \)
\( (-1;2) \)