Need help for proving: $f(f^{−1}(A)) ⊆ A$.
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
121993
Prove that $f$ is one-to-one iff $f \circ h = f \circ k$ implies $h = k$.
158862
Show that $a(-1) = (-1)a = -a $.
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
32929
Questions about proving $\lnot \lnot a = a$
33030
Proof that $\inf A = -\sup(-A)$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
48275
$f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
102553
How to show that $f(z) = f(i)$
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
52787
If $\bigcup F = A$ then $A\in F$ then prove that $A$ has exactly one element
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $