Question

Prove that the functions $F$ and $G$ which have same domain and range are equal.

score 835 · Answer 1 · 2026-04-15 23:33:48

Prove that the functions $F$ and $G$ which have same domain and range are equal.

Published on 15 Apr 2026 - 23:33

score 38 · Answer 2 · 2026-04-16 00:45:05

Verification of $\forall x \in \mathbb{R},(\bigg \lfloor \frac{\lfloor \frac{x}{2} \rfloor}{2} \bigg \rfloor = \lfloor \frac{x}{4} \rfloor )$

score 42 · Answer 3 · 2026-04-14 10:50:35

42

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Intermediate Value Theorem (Connectivity)

Published on 14 Apr 2026 - 10:50

score 108 · Answer 4 · 2026-04-16 00:37:25

108

Views

Calculate the total number of sign changes

Published on 16 Apr 2026 - 0:37

score 81 · Answer 5 · 2026-04-16 13:53:47

81

Views

Solution Verification: Factoring $\left|\begin{smallmatrix}x&y&z\\x^p&y^p&z^p\\x^{p^2}&y^{p^2}&z^{p^2}\end{smallmatrix}\right|$ over $\mathbb{Z}_p.$

Published on 16 Apr 2026 - 13:53

score 322 · Answer 6 · 2026-04-14 00:21:01

322

Views

Any finite connected graph with every vertex has degree $\ge 2$ has a circuit

Published on 14 Apr 2026 - 0:21

score 70 · Answer 7 · 2026-04-11 12:17:25

70

Views

How do I show that $f^{'}$ exist and is continuous for every $x \in \mathbb{R}$.

Published on 11 Apr 2026 - 12:17

score 441 · Answer 8 · 2026-04-13 20:03:53

441

Views

Proof Check: $x \leq y+ \epsilon$ for all $\epsilon >0$ iff $x \leq y$.

Published on 13 Apr 2026 - 20:03

score 105 · Answer 9 · 2026-04-13 18:51:13

105

Views

Did I do something wrong in solving the functional equation $2f(x+y)+6y^3=f(x+2y)+x^3$ or does it have no solutions?

Published on 13 Apr 2026 - 18:51

score 86 · Answer 10 · 2026-04-15 09:40:35

86

Views

topology quotient and upper semicontinuous sets.

Published on 15 Apr 2026 - 9:40

score 2.1k · Answer 11 · 2026-04-16 05:54:19

2.1k

Views

Let $f(x)$ be a polynomial of degree $8$ such that $f(r)=\frac1r$, for $r=1,2,3,\ldots,9$. Find $\frac1{f(10)}$.

Published on 16 Apr 2026 - 5:54

score 76 · Answer 12 · 2026-04-14 13:25:13

76

Views

Elements of same additive order are associates in $\mathbb{Z}_m $?

Published on 14 Apr 2026 - 13:25

score 56 · Answer 13 · 2026-04-24 00:22:14

56

Views

Proof verification: circle pawn problem

Published on 24 Apr 2026 - 0:22

score 944 · Answer 14 · 2026-04-12 11:45:55

944

Views

Prove that for any set $A$, $A = \bigcup \mathscr P (A)$.

Published on 12 Apr 2026 - 11:45

score 589 · Answer 15 · 2026-04-12 15:25:30

589

Views

Grimmet Introduction to Probability exercise 1.52 : Bayes Theorem Question

Published on 12 Apr 2026 - 15:25

List Question

Prove that the functions $F$ and $G$ which have same domain and range are equal.

Verification of $\forall x \in \mathbb{R},(\bigg \lfloor \frac{\lfloor \frac{x}{2} \rfloor}{2} \bigg \rfloor = \lfloor \frac{x}{4} \rfloor )$

Intermediate Value Theorem (Connectivity)

Calculate the total number of sign changes

Solution Verification: Factoring $\left|\begin{smallmatrix}x&y&z\\x^p&y^p&z^p\\x^{p^2}&y^{p^2}&z^{p^2}\end{smallmatrix}\right|$ over $\mathbb{Z}_p.$

Any finite connected graph with every vertex has degree $\ge 2$ has a circuit

How do I show that $f^{'}$ exist and is continuous for every $x \in \mathbb{R}$.

Proof Check: $x \leq y+ \epsilon$ for all $\epsilon >0$ iff $x \leq y$.

Did I do something wrong in solving the functional equation $2f(x+y)+6y^3=f(x+2y)+x^3$ or does it have no solutions?

topology quotient and upper semicontinuous sets.

Let $f(x)$ be a polynomial of degree $8$ such that $f(r)=\frac1r$, for $r=1,2,3,\ldots,9$. Find $\frac1{f(10)}$.

Elements of same additive order are associates in $\mathbb{Z}_m $?

Proof verification: circle pawn problem

Prove that for any set $A$, $A = \bigcup \mathscr P (A)$.

Grimmet Introduction to Probability exercise 1.52 : Bayes Theorem Question

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