1003187206
Level:
C
How many \( x \)-intercepts does the graph of \( f(x)=\left|-|2-x|- 2\right| \) have?
\( 0 \)
\( 2 \)
\( 1 \)
\( 4 \)
C
1003187205
Level:
C
Let \( f(x)=\left|3|2x-1|-9\right| \). The number of argument values \( x \) for which \( f(x)=2 \) is:
\( 4 \)
\( 2 \)
\( 3 \)
\( 1 \)
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.
\[ \log_2^2(x-2)< \log_2(x-2) \]
\( (3,4) \)
\( (0,1) \)
\( (-\infty,4) \)
\( (-\infty,1) \)