1003044808
Level:
A
Find the domain of the equation \( \frac{3x+2}{\frac x3}=1 \).
\( \mathbb{R}\setminus \{0\} \)
\( \mathbb{R} \)
\( \mathbb{R}\setminus \{-\frac23\} \)
\( \mathbb{R}\setminus \{-\frac23;0\} \)
Rational equations and inequalities
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 \( \frac{x+2}{x^2-x-6}=\frac{x^2-x-6}{x+2} \).
\( \mathbb{R}\setminus\{-2;3\} \)
\( \mathbb{R}\setminus\{-2;3;4\} \)
\( \mathbb{R}\setminus\{-2\} \)
\( \mathbb{R}\setminus\{-2;4\} \)
1103044803
Level:
A
Given graphs of the functions \( f(x)= x^2-x-6 \) and \( g(x) = x+2 \), find the domain of the equation \( \frac{x+2}{x^2-x-6}=1 \).
\( \mathbb{R}\setminus\{-2;3\} \)
\( \mathbb{R}\setminus\{-2;4\} \)
\( \mathbb{R}\setminus\{0\} \)
\( \mathbb{R}\setminus\{-2\} \)
1103044802
Level:
A
Given graphs of the functions \( f(x)=x^2-4x \) and \( g(x) = 4x^2-16x+12 \), find the domain of the equation \( \frac{4x^2-16x+12}{x^2-4x}=6 \).
\( \mathbb{R}\setminus\{0;4\} \)
\( \mathbb{R}\setminus\{1;3\} \)
\( \mathbb{R}\setminus\{0;1;3;4\} \)
\( \mathbb{R}\setminus\{2\} \)
1103044801
Level:
A
Given graphs of the functions \( f(x) =2x^2-2x-4 \) and \( g(x) = 2x+2 \), find the domain of the equation\( \frac{2x^2-2x-4}{2x+2} = 10 \).
\( \mathbb{R}\setminus\{-1\} \)
\( \mathbb{R}\setminus\{-1;2\} \)
\( \mathbb{R}\setminus\{-1;2;3\} \)
\( \mathbb{R}\setminus\{-1;3\} \)
1003029001
Level:
B
Find the solution set of the inequality.
\[ \left(x^2+1\right)\left(x^2+3\right)\geq0 \]
\( \mathbb{R} \)
\( (-\infty;-1]\cup[1;\infty) \)
\( (-\infty;-1)\cup(1;\infty) \)
\( (-\infty;-\sqrt3]\cup[\sqrt3;\infty) \)
\( \emptyset \)
1003029104
Level:
B
Find the domain of the expression on the left side of the inequality.
\[ \frac{x^3-x^2+1}{\left(x^2+9\right)\left(x^3-1\right)}>0 \]
\( \mathbb{R}\setminus\left\{1\right\} \)
\( \mathbb{R} \)
\( \mathbb{R}\setminus\left\{\pm1\right\} \)
\( \mathbb{R}\setminus\left\{\pm3;\pm1\right\} \)