1003020603
Level:
A
Find the domain of the expression.
\[
\sqrt{-x^2+x+20}
\]
\(\left[-4;5\right]\)
\(\left(-\infty;-4\right]\cup\left[5;\infty\right)\)
\(\emptyset\)
\(\left[-5;4\right]\)
Radical equations and inequalities
1003020602
Level:
A
Find the domain of the expression.
\[
\frac{\sqrt{x^2-x-6}}{x^2-7x+10}
\]
\(\left(-\infty;-2\right]\cup\left[3;5\right)\cup\left(5;\infty\right)\)
\(\left(-\infty;-2\right)\cup\left(3;\infty\right)\)
\(\left(-\infty;-2\right)\cup\left(3;5\right)\cup\left(5;\infty\right)\)
\(\left(-\infty;2\right)\cup\left(3;5\right)\cup\left(5;\infty\right)\)
1003020601
Level:
A
Find the domain of the expression.
\[
\frac1{\sqrt{5x^2+7x-6}}
\]
\(\left(-\infty;-2\right)\cup\left(\frac35;\infty\right)\)
\(\left(-2;\frac35\right)\)
\(\left(-\infty;-2\right]\cup\left[\frac35;\infty\right)\)
\(\left[-2;\frac35\right]\)
1003020702
Level:
B
Find the solution of the inequality.
\[
\sqrt{3x^2-x+7}\geq2
\]
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\left(-\frac13;\frac73\right)\)
\(x\in\mathbb{R}\setminus\{2\}\)
1003020701
Level:
B
Find the solution of the inequality.
\[
\sqrt{-2x^2+x+5}\geq5
\]
\(x\in\emptyset\)
\(x\in[-1;5]\)
\(x\in\left(-\frac12;\frac52\right)\)
\(x\in\mathbb{R}\)
1003019902
Level:
A
Find the solution of the equation.
\[
\sqrt{x^2-4x+3}=\sqrt{x^2-6x+3}
\]
\(x\in\{0\}\)
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\mathbb{R}\setminus\{0\}\)
1003019901
Level:
A
Find the solution of the equation.
\[
\sqrt{-3x^2+2x+5}=3
\]
\(x\in\emptyset\)
\(x\in[-2;2]\)
\(x\in\{-2;2\}\)
\(x\in\mathbb{R}\)
9000034903
Level:
A
Find all \(x\in \mathbb{R}\)
for which the following expression is undefined.
\[
\sqrt{\left (3x + 4 \right ) \left (\frac{1}
{5} - x\right )}
\]
\(\left (-\infty ;-\frac{4}
{3}\right )\cup \left (\frac{1}
{5};\infty \right )\)
\(\left [ -\frac{4}
{3}; \frac{1}
{5}\right ] \)
\(\left (-\infty ;-\frac{4}
{3}\right ] \cup \left [ \frac{1}
{5};\infty \right )\)
\(\left (-\frac{4}
{3}; \frac{1}
{5}\right )\)
9000034901
Level:
A
Find the domain of the following expression.
\[
\sqrt{\left (2x - 3 \right ) \left (3x + 1 \right )}
\]
\(\left (-\infty ;-\frac{1}
{3}\right ] \cup \left [ \frac{3}
{2};\infty \right )\)
\(\left [ -\frac{1}
{3}; \frac{3}
{2}\right ] \)
\(\left (-\frac{1}
{3}; \frac{3}
{2}\right )\)
\(\left (-\infty ;-\frac{1}
{3}\right )\cup \left (\frac{3}
{2};\infty \right )\)
9000033702
Level:
A
Find the domain of the following expression.
\[
\sqrt{-x^{2 } + 7x - 12} -\frac{1}
{x}
\]
\([ 3;4] \)
\(\mathbb{R}\setminus \left \{0\right \}\)
\(\mathbb{R}\setminus \left \{0;3;4\right \}\)
\(\left (3;4\right )\)
\(\left (-\infty ;3\right )\cup \left (4;\infty \right )\)
\(\left (-\infty ;3] \cup [ 4;\infty \right )\)