1003170902
Level:
C
Find the solution set of the following inequality.
\[ \log_{0.1}\frac{2-x}{x+1}>0 \]
\( \left(\frac12,2\right) \)
\( (-\infty,-1)\cup\left(\frac12,\infty\right) \)
\( \left(-1,\frac12 \right) \)
\( (-1,2) \)
C
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.
\( a=c-1\wedge b=d+4 \)
\( a=c+1\wedge b=d-4 \)
\( a=c-4\wedge b=d+1 \)
\( a=c+4\wedge b=d-1 \)
1003138404
Level:
C
Find the range of the function \( f(x)=\left|\log_3x\right| \).
\( [ 0,\infty ) \)
\( (0,\infty) \)
\( (-\infty,\infty) \)
\( [1,\infty) \)
1003138403
Level:
C
Find the domain of the function \( f(x)=\sqrt{\log_2x} \).
\( [ 1,\infty ) \)
\( (0,\infty ) \)
\( [ 0,\infty) \)
\( (1,\infty) \)
1103138402
Level:
C
From the following functions choose the one which is graphed in the picture.
\( k(x) = \log_2|x| \)
\( m(x) = |\log_2 x| \)
\( f(x) = \log_2\sqrt x \)
\( g(x) = \sqrt{\log_2 x} \)
1103138401
Level:
C
From the following functions choose the one which is graphed in the picture.
\( f(x)=\left|\log_{\frac12}x\right| \)
\( g(x) = \log_{\frac12}|x| \)
\( k(x)=\log_{\frac12}\sqrt x \)
\( m(x)=\sqrt{\log_{\frac12}x} \)