maximum

256 Questions
128 Answers

0

105

0

+818

help domain

Find the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c+12x+x^2}$ has a domain of all real numbers.

maximum 9 oct. 2023

0

111

0

+818

need help

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
$$f(x) = 2x^2-8x+1.$$
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

maximum 7 oct. 2023

0

93

0

+818

domain

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

maximum 7 oct. 2023

0

110

0

+818

domain question

If $f(x)$ is a function whose domain is $[-8,8]$, and $g(x)=f\left((x^2 - 2)/(x + 1)\right)$, then the domain of $g(x)$ is an interval of what width?

maximum 7 oct. 2023

0

80

1

+818

help plz

Find the sum of all real numbers $x$ that are not in the domain of the function $$f(x) = \frac{1}{x^2+7} + \frac{1}{x^3 - x^4} + \frac{1}{x^2 - 3x + 2}.$$

maximum 7 oct. 2023

0

116

0

+818

need help with domain

Find the number of real numbers that are not in the domain of the function $$f(x) = \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3}.$$

maximum 7 oct. 2023

0

106

0

+818

help with domain plz

Find the smallest real number $x$ in the domain of the function $$f(x) = \sqrt{(x-3)^2-(x+3)^2}.$$

maximum 7 oct. 2023

0

102

1

+818

range of function

The domain of the function $f(x) = \sqrt{25-x^2}+\sqrt{x-2} + \frac{1}{\sqrt{1 - x}}$ is an interval of what width?

maximum 7 oct. 2023

0

65

1

+818

range

The range of the function $f(x) = \frac{2}{2+4x^2-4x}$ can be written as an interval $(a,b]$. What is $a+b$?

maximum 7 oct. 2023

0

103

0

+818

help hard inequality

Find all $x$ such that neither $2x-5$ nor $-20x+13x-7$ is in the interval $(8,12)$.

maximum 6 oct. 2023

+818

-1

Do not post AoPS homework.

maximum20 janv. 2025