maximum

260 Questions
128 Answers

-2

125

0

+835

domain

Find the domain of the function $f(x)=\frac{x+6}{\sqrt{x^2}-3x-4} + \sqrt{x - 8} + \frac{1}{\sqrt{(x + 4)(x + 3)}}$.

maximum Sep 3, 2023

-2

152

0

+835

domain question

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.

maximum Sep 3, 2023

-2

92

1

+835

graphing question

The graphs of $y=x^4$ and $y=5x^2-6+4x^2$ intersect at four points with $x$-coordinates $\pm \sqrt{m}$ and $\pm \sqrt{n}$, where $m > n$. What is $m-n$?

maximum Sep 1, 2023

-2

146

1

+835

positive integers

The difference between two positive integers is $6$ and their product is $40$. What is the sum of the integers?

maximum Sep 1, 2023

-2

127

1

+835

Help plz!

Real numbers $x$ and $y$ have an arithmetic mean of $18$ and a geometric mean of $\sqrt{47}$. Find $x^2+y^2$.

maximum Sep 1, 2023

-2

162

2

+835

quadratic

Help this is a question about quadratic
The quadratic equation $ax^2+20x+c=4x$ has exactly one solution. If $a+c=20$, and $a

maximum Aug 31, 2023

-2

127

2

+835

help plz

I cant solve this it's hard
Solve the inequality
\[\dfrac{x+1}{x+2}>\dfrac{3x+4}{2x+9}+\dfrac{1}{3}.\]

maximum Aug 30, 2023

-3

131

5

+835

graph of rational function

The graph of $y = \frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic. (Assume that the grid lines are at integers.)
The horizontal asymptote is $y = 2,$ and the only vertical asymptote is $x = -2.$ read more ..

●●●●●

maximum Aug 28, 2023

-3

155

0

+835

asymptotes

For what values of the constant $c$ does the graph of $f(x) = \frac{x^2-x+c}{x^2+8x-50}$ have exactly one vertical asymptote?
Enter all possible values, separated by commas.

maximum Aug 28, 2023

+835

-1

Do not post AoPS homework.

maximumJan 20, 2025