1003044501
Level:
A
Identify the solution of the equation.
\[ 2^{x^2-x-3}=8. \]
\( x_1=3 \), \( x_2=-2 \)
\( x_1=-3\), \( x_2=2 \)
\( x_1=0 \), \( x_2=1 \)
\( x_1=0 \), \( x_2=-1 \)
A
1003047003
Level:
A
We are given the equation \( \frac{8x}{x+2}+\frac{12}{x+2}=\frac{2x}{x+2} \). Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.
\( 8x+12=2x \)
\( \frac{4x}{x+2}+\frac6{x+2}=\frac x{x+2} \)
\( \frac{6x}{x+2}=-\frac{12}{x+2} \)
\( \frac x{x+2}=-\frac2{x+2} \)
1003047002
Level:
A
We are given the equation \( 1-\frac{5-x}2=\frac x4 \). Decide which of the following equations is equivalent to the given equation, i.e. which of the following equations was obtained from the given equation by equivalent transformations.
\( -6+2x=x \)
\( -6-2x=x \)
\( -9+2x=x \)
\( -6-x=x \)
1003047001
Level:
A
We are given the equation \( 2x^2+10x=8x+2x^2 \). Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.
\( 2x+10=8+2x \)
\( 10x=8x \)
\( 2x^2+2x=2x^2 \)
\( x^2+5x=4x+x^2 \)
1003044809
Level:
A
Find the domain of the equation \( \frac{2x+5}{x-2}=\frac1{x^2-1} \).
\( \mathbb{R}\setminus\{-1;1;2\} \)
\( \mathbb{R}\setminus\{1;2\} \)
\( \mathbb{R}\setminus\{-\frac52;-1;1\} \)
\( \mathbb{R}\setminus\{2\} \)
1003044808
Level:
A
Find the domain of the equation \( \frac{3x+2}{\frac x3}=1 \).
\( \mathbb{R}\setminus \{0\} \)
\( \mathbb{R} \)
\( \mathbb{R}\setminus \{-\frac23\} \)
\( \mathbb{R}\setminus \{-\frac23;0\} \)
1003044807
Level:
A
Find the domain of the equation \( \frac{x+1}{x^2-3}=\frac{x^2+x-2}{2x+8} \).
\( \mathbb{R}\setminus\{-4;-\sqrt3;\sqrt3\} \)
\( \mathbb{R}\setminus\{-2;-1;1\} \)
\( \mathbb{R}\setminus\{-4;\sqrt3\} \)
\( \mathbb{R}\setminus\{-4\} \)
1003044806
Level:
A
Find the domain of the equation \( \frac{(x-1)(x+2)}{(x-1)(x+3)}=\frac1x \).
\( \mathbb{R}\setminus\{-3;0;1\} \)
\( \mathbb{R}\setminus\{-3;0\} \)
\( \mathbb{R}\setminus\{-3;-2;0\} \)
\( \mathbb{R}\setminus\{-3;1\} \)
1103044805
Level:
A
Given graphs of the functions \( f(x)=-x^2-x+6 \) and \( g(x) =x^2-4x+4 \), find the domain of the equation \( \frac{-x^2-x+6}{x^2-4x+4} =-2 \).
\( \mathbb{R}\setminus\{2\} \)
\( \mathbb{R}\setminus\{-3;2\} \)
\( \mathbb{R}\setminus\{-3;-0.5;2\} \)
\( \mathbb{R}\setminus\{-2\} \)
1103044804
Level:
A
Given graphs of the functions \( f(x) = x^2-x-6 \) and \( g(x) = x+2 \), find the domain of the equation \( \frac{x+2}{x^2-x-6}=\frac{x^2-x-6}{x+2} \).
\( \mathbb{R}\setminus\{-2;3\} \)
\( \mathbb{R}\setminus\{-2;3;4\} \)
\( \mathbb{R}\setminus\{-2\} \)
\( \mathbb{R}\setminus\{-2;4\} \)