Finding value of $c$ such that the range of the rational function $f(x) = \frac{x^2 + x + c}{x^2 + 2x + c}$ does not contain $[-1, -\frac{1}{3}]$
138164
If the range of $f(x)= \frac{x^2+x+c}{x^2+2x+c}, x\in \mathbb R$ is $\left[\frac 56, \frac 32\right]$ then what is $c$?
54078
The minimum value of $\frac{(x+\frac{1}{x})^6-(x^6+\frac{1}{x^6})-2}{(x+\frac{1}{x})^3+x^3+\frac{1}{x^3}}$
144859
Finding parameters for $f(x) = x^2 + 2(m − a)x + 3am −2 = 0$ that satisfy a condition.
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
73607
Find the residue at $z=-2$ for $g(z) = \frac{\psi(-z)}{(z+1)(z+2)^3}$
112709
$\frac{1}{x-a} + \frac{1}{x-b} + \frac{1}{x-c} = 0 $ has precisely two real roots
156646
If $x$ is rational then $\,x+\frac{1}x \,$ is an integer $\iff x = \pm 1$
87041
How to determine with certainty that a function has no elementary antiderivative?
131561
Find the value of $\left[\frac{1}{\sqrt 2}+\frac{1}{ \sqrt 3}+......+\frac{1}{\sqrt {1000}}\right]$
20055
Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
40534
What is $(-1)^{\frac{2}{3}}$?
158605
Finding The Laurent Series for $\sin(\frac{z}{1+z})$ at $z = -1.$
113045
How do I find the inverse of $f(x) = \frac{x}{x^2 + 1}$
101918
Let $f(x)=ax^2+bx+c$ where $a,b,c$ are real numbers. Suppose $f(-1),f(0),f(1) \in [-1,1]$. Prove that $|f(x)|\le \frac{3}{2}$ for all $x \in [-1,1]$.
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
48252
Range of function Involving Modulus Quantity.
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$