1003138404
Level:
C
Find the range of the function \( f(x)=\left|\log_3x\right| \).
\( [ 0;\infty ) \)
\( (0;\infty) \)
\( (-\infty;\infty) \)
\( [1;\infty) \)
C
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.
\( f(x)=\left|\log_{\frac12}x\right| \)
\( g(x) = \log_{\frac12}|x| \)
\( k(x)=\log_{\frac12}\sqrt x \)
\( m(x)=\sqrt{\log_{\frac12}x} \)
1003124906
Level:
C
The number \( \left(\sqrt7+1\right)^4-\left(\sqrt7-1\right)^4 \) equals:
\( 64\sqrt7 \)
\( 32\sqrt7 \)
\( \sqrt7 \)
\( 2 \)
1003124905
Level:
C
Numbers \( \left(2^2\right)^{\left(2^2\right)} \), \( \left(2\right)^{\left({2^2}^2\right)} \), \( \left({2^2}^2\right)^2 \), \( \left(2\right)^{\left(2^2\right)^2} \) were written on the board. How many different numbers are represented by these records?
\( 2 \)
\( 3 \)
\( 4 \)
\( 1 \)
1003124904
Level:
C
The number\( \sqrt[4]{\left( \sqrt3-\sqrt2 \right)^4}+\sqrt[4]{\left( \sqrt2-\sqrt5 \right)^4}+\sqrt[3]{\left( \sqrt3-\sqrt5 \right)^3} \) equals:
\( 2\sqrt3 - 2\sqrt2 \)
\( 2\sqrt5 - 2\sqrt2 \)
\( 2\sqrt3 - 2\sqrt5 \)
\( 2\sqrt5 - 2\sqrt3 \)
1003124903
Level:
C
The number \( \left( \sqrt2+1 \right)^4 \) is greater than the number \( \left( \sqrt2-1 \right)^4 \) by:
\( 24\sqrt2 \)
\( 12\sqrt2 \)
\( 2 \)
\( 4\sqrt2 \)
1003124902
Level:
C
Rationalizing the denominator \( \frac1{\left(2-\sqrt3\right)^3} \) you get:
\( 26+15\sqrt3 \)
\( 27+30\sqrt3 \)
\( 14+7\sqrt3 \)
\( 27+24\sqrt3 \)
1003107511
Level:
C
Find the solution set of the following quadratic equation in the complex plane.
\[ 2x^2-x=3\mathrm{i}x+2 \]
\( \left\{-\frac12+\frac12\mathrm{i}; 1+\mathrm{i} \right\} \)
\( \left\{-\frac12+\mathrm{i}; 1+\frac12\mathrm{i} \right\} \)
\( \left\{\frac12-\frac12\mathrm{i}; -1-\mathrm{i} \right\} \)
\( \left\{\frac12-\mathrm{i}; -1-\frac12\mathrm{i} \right\} \)
\( \left\{-\frac12-\frac12\mathrm{i}; 1-\mathrm{i} \right\} \)
\( \left\{\frac12+\mathrm{i}; -1+\frac12\mathrm{i} \right\} \)