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1003138404

Level:

Find the range of the function

f (x) = | \log_{3} x |

[0; \infty)

(0; \infty)

(- \infty; \infty)

[1; \infty)

1003138403

Level:

Find the domain of the function

f (x) = \sqrt{\log_{2} x}

[1; \infty)

(0; \infty)

[0; \infty)

(1; \infty)

1103138402

Level:

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:

From the following functions choose the one which is graphed in the picture.

f (x) = | \log_{\frac{1}{2}} x |

g (x) = \log_{\frac{1}{2}} | x |

k (x) = \log_{\frac{1}{2}} \sqrt{x}

m (x) = \sqrt{\log_{\frac{1}{2}} x}

1003124906

Level:

The number

{(\sqrt{7} + 1)}^{4} - {(\sqrt{7} - 1)}^{4}

equals:

64 \sqrt{7}

32 \sqrt{7}

\sqrt{7}

2

1003124905

Level:

Numbers

{(2^{2})}^{(2^{2})}

{(2)}^{({2^{2}}^{2})}

{({2^{2}}^{2})}^{2}

{(2)}^{{(2^{2})}^{2}}

were written on the board. How many different numbers are represented by these records?

2

3

4

1

1003124904

Level:

The number

\sqrt[4]{{(\sqrt{3} - \sqrt{2})}^{4}} + \sqrt[4]{{(\sqrt{2} - \sqrt{5})}^{4}} + \sqrt[3]{{(\sqrt{3} - \sqrt{5})}^{3}}

equals:

2 \sqrt{3} - 2 \sqrt{2}

2 \sqrt{5} - 2 \sqrt{2}

2 \sqrt{3} - 2 \sqrt{5}

2 \sqrt{5} - 2 \sqrt{3}

1003124903

Level:

The number

{(\sqrt{2} + 1)}^{4}

is greater than the number

{(\sqrt{2} - 1)}^{4}

by:

24 \sqrt{2}

12 \sqrt{2}

2

4 \sqrt{2}

1003124902

Level:

Rationalizing the denominator

\frac{1}{{(2 - \sqrt{3})}^{3}}

you get:

26 + 15 \sqrt{3}

27 + 30 \sqrt{3}

14 + 7 \sqrt{3}

27 + 24 \sqrt{3}

1003107511

Level:

Find the solution set of the following quadratic equation in the complex plane.

2 x^{2} - x = 3 i x + 2

{- \frac{1}{2} + \frac{1}{2} i; 1 + i}

{- \frac{1}{2} + i; 1 + \frac{1}{2} i}

{\frac{1}{2} - \frac{1}{2} i; - 1 - i}

{\frac{1}{2} - i; - 1 - \frac{1}{2} i}

{- \frac{1}{2} - \frac{1}{2} i; 1 - i}

{\frac{1}{2} + i; - 1 + \frac{1}{2} i}

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