1003118004
Level:
C
The number \( \sqrt{3-2\sqrt2} \) equals:
\( \sqrt2-1 \)
\( 1-\sqrt2 \)
\( \sqrt2 \)
\( \sqrt3-\sqrt{2\sqrt2} \)
C
1003118003
Level:
C
Give the multiplicative inverse of \( \frac{\sqrt[3]4-\sqrt[3]2}2 \).
\( 2\sqrt[3]2 + 2 +\sqrt[3]4 \)
\( \sqrt[3]{12}+2+\sqrt[3]4 \)
\( 2\sqrt[3]{12}+2+\sqrt[3]4 \)
\( \sqrt[3]{2}+2+\sqrt[3]4 \)
1003118002
Level:
C
The number \( \sqrt{7-4\sqrt3} + \sqrt{7+4\sqrt3} \) is equal to:
\( 4 \)
\( \sqrt{14} \)
\( 16 \)
\( 8\sqrt3 \)
1003118001
Level:
C
The number \( 3\sqrt[3]3\cdot\sqrt[4]{3\sqrt[3]3}\cdot\sqrt[5]{3\sqrt[3]3\cdot\sqrt[4]{3\sqrt[3]3}} \) is equal to:
\( 9 \)
\( 3 \)
\( \sqrt3 \)
\( \sqrt[3]3 \)
1103124502
Level:
C
Identify which of the graphs below represents the function \( f(x)=\left|\frac{1-2x}{x-4}\right|;\ x\in [-\frac52;\frac52] \).
1103124602
Level:
C
Let \( f(x)=\frac{x^2-x-6}{x^2-9} \). One of the following pictures shows a part of the graph of \( f \). Choose the picture.
1003118307
Level:
C
Identify which of the following functions has the maximum at \( x=-\frac12 \).
\( m(x)=-\left|\frac{4x+2}{x-2}\right| \)
\( g(x)=\left|-\frac{5x+10}{2x-1}\right| \)
\( f(x)=-\left|\frac{2x+1}{4x+2}\right| \)
\( h(x)=-\left|\frac{x+1}{2x-2}\right| \)
1003118306
Level:
C
Find the true statement about the function \( f(x)=\left|\frac{4x-4}{2x-1}\right| \).
The domain of the function \( f \) is the set \( \left(-\infty;\frac12\right)\cup\left(\frac12;\infty\right) \).
The range of the function \( f \) is the set \( [0;2)\cup(2;\infty) \).
The function \( f \) has the minimum at \( x=4 \).
The function \( f \) is an injective (one-to-one) function.
1003118305
Level:
C
Find the false statement about the function \( f(x)=\left|\frac1{2-3x}-3\right| \).
The domain of the function \( f \) is the set \( \left(-\infty;\frac32\right)\cup\left(\frac32;\infty\right) \).
The range of the function \( f \) is the interval \( \left[0;\infty\right) \).
The function \( f \) has the minimum at \( x=\frac59 \).
The function \( f \) is bounded below.
1003118304
Level:
C
Identify which of the following functions is bounded.
\( h(x)=\frac{3x-6}{2x-4} \)
\( f(x)=\frac{3x-6}{2x} \)
\( g(x)=3-\frac6{2x} \)
\( m(x)=\left|\frac{4x-3}{2x-6}\right| \)