1003123901
Level:
B
Given \( f(x)=\frac{2x+3}{x-5} \), find the true statement in the following list.
\( f(x)=2+\frac{13}{x-5} \)
\( f(x)=2+\frac3{x-5} \)
\( f(x)=2x+\frac3{x-5} \)
\( f(x)=3+\frac{2x}{x-5} \)
B
1003124601
Level:
B
Let \( f(x)=\frac{2x}{x^2-1} \). Find the true statement.
\( \forall x\in(-\infty;-1)\cup(0;1)\colon f(x) < 0 \).
The domain of \( f \) is \( (-\infty;1)\cup(1;\infty) \).
\( \forall x\in(-1;1)\colon f(x) \leq 0 \).
The domain of \( f \) is \( (-\infty;-1)\cup(-1;0)\cup(0;1)\cup(1;\infty) \).
1003118303
Level:
B
Find the false statement about the function \( f(x)=\frac{4x+1}{3-2x};\ x\in[2;\infty) \).
The function \( f \) has no minimum.
The function \( f \) is increasing.
The function \( f \) has no maximum.
The function \( f \) is bounded.
1003118302
Level:
B
Find the true statement about the function \( f(x)=1-\frac2{0.5x-1};\ x\in[-3;1)\cup(2;6] \).
The function \( f \) has no maximum.
The function \( f \) has the maximum at \( x=6 \).
The function \( f \) has the minimum at \( x=-3 \).
The function \( f \) is bounded.
1003118301
Level:
B
Find the true statement about the function \( f(x)=-1+\frac3{2x-6} \).
The function \( f \) is decreasing on the interval \( (3;\infty) \).
The function \( f \) is decreasing on the interval \( (-3;\infty) \).
The function \( f \) is decreasing on the interval \( (-\infty;6) \).
The function \( f \) is decreasing on the interval \( (-1;\infty) \).
1003032210
Level:
B
Which of the given numbers belongs to the interval \( (-5;5) \)?
\( 3\left(\sqrt{0.1}\right)^4\cdot\left(\sqrt3\right)^8 \)
\( \left(3\sqrt{5}\right)^2-\left(\sqrt2\right)^6 \)
\( \left(\sqrt3\right)^4-\left(\sqrt2\right)^4 \)
\( 3\left(\sqrt{0.1}\right)^4+\left(\sqrt3\right)^8 \)
1003032209
Level:
B
What is the value of \( \left(2^{\sqrt7-\sqrt2}\right)^{\sqrt7+\sqrt2} \)?
\( 32 \)
\( 2^{\sqrt{45}} \)
\( 2^9 \)
\( 1024 \)
1003032208
Level:
B
Write the number \( \frac13\cdot9^{\pi+\frac12}:81^{2\pi} \) in the form of \( a^x \), where \( a \) is a natural number.
\( 3^{-6\pi} \)
\( 3^{6\pi} \)
\( 3^{-\frac12+3\pi} \)
\( 9^{-\frac12+3\pi} \)
1003032207
Level:
B
Let \( x=2^{4\sqrt2} \), \( y=4^{\frac{\sqrt2}2} \) and \( z=8^{-\frac{\sqrt2}3} \). Which two numbers are multiplicative inverses of each other?
\( y\), \( z \)
\( x\), \( y \)
\( x\), \( z \)
no two numbers
1003032206
Level:
B
Simplifying the expression \( \frac{\left(\frac13\right)^{-3}\cdot27^{-2}}{9^{-5}\cdot\sqrt{3^4}} \) we will get:
\( 3^5 \)
\( 3^{-11} \)
\( 3^2 \)
\( 3^{-5} \)