Prove $f(x)=g(x)$ has at least 1 solution $c$ in $(a,b)$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
76790
Condition to guarantee $f=0$ on $[a,b]$
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
54729
Prove that $f$ has a fixed point .
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
62455
Prove Equivalence Relation in G
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
48780
How t show $f=g$ almost everywhere
91786
Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$