Hello guys. I have a doubt trying to solve this problem:

"Let f,g be functions such that (gof)(x) = x for all x in the Domain of f and (fog)(y) = y for all y in the domain of f. Prove that g= f^-1."

This is the 24th problem in section 1.1 of Bartle & Sherbert's intro to real analysis (if you want a little more info about the problem).

I got stucked and looked upon the solutions for a hint.

I understoos nearly all the process but I don't quite get the end of the proof.

First, I proved that (gof) is injective, so I can use the fact that f is injective, and I also proved that (fog) is surjective to use that g is surjective.

The part that I didn't get was to see that f: Dom(f) --> Dom(g) is bijective and therefore g=f^-1.

How can I know that f: Dom(f) --> Dom(g) ?

I’m 20 and was taken out of traditional schooling in 6th grade for medical reasons. I’m currently rebuilding my academics, especially math, through an intensive remedial course during my gap year. After that, I plan to start community college and eventually apply to transfer to a strong university.
I’m planning to take the SAT in about two years, and my goal is 1500+. I know that’s ambitious given my starting point, but I’m committed to putting in the work.
How would you recommend preparing over that time? Should I focus entirely on my foundations for now, or introduce SAT-specific practice along the way? I’d especially love to hear from anyone who started with significant math gaps and eventually scored well. What helped you most?

We got this assignment and it's due in 20 minutes, but none of us can seem to solve it. Even just the process or steps to solve it is ok. I just need some backbone.

Question b) Trying to solve for the partial derivative for theta with respect to r is giving me an aneurism, someone please help. Have exam in 3 hours

Uhh I tried doing it in the corner but I guess I suck at imagining diagrams. If anyone could help me visualize it better or just explain what they do that would be amazing, thanks!

So, I’m taking a CAD class, and doing great in it so far. But I have to take a midterm, and while reviewing, I remember the very first lab I ever did. It was the only one I struggled SEVERELY with, and it’s not because of the CAD portion, but the geometry. I haven’t done geometry since I was a 9th grader, and CAD only accepts angles that are on the positive x-axis. How to solve these? I tried looking everywhere, and I just can’t figure it out. Like angle HG on positive x? Angle GF? Angle FE?

im really stuck on section two ik it’s pretty basic stuff but word problems mess my brain up. im trying to write the equation in that form but idk how

I'm trying to work out the measurement marked in red, to see if my monitor will fit this desk.

I played silly buggers during trigonometry and now I'm paying for it 🫠

Im in my last year in the netherlands of VWO 6 and am really struggling with mathematics. Last year i barely passee with a 4,5 and im really scared i will fail because i find it very difficult. Its not possible to repeat so i really need help on how to quickly improve between now and 6 weeks

Not a homework question, but hopefully useful here. I'm a math teacher and made a free tool for studying from a graded test before a retake or final.

Take photos of your graded test, paste the site's prompt into ChatGPT, Gemini or Claude with the photos, paste the answer back, and check that it read your test correctly. It builds a step-by-step walkthrough of every question that shows the exact step that went wrong, plus 10 new practice problems with the same traps and a printable answer key. Every answer is double-checked in your browser by plugging in numbers, since AI makes arithmetic mistakes.

It only works on tests that are already graded. It's for learning from mistakes, not getting answers.

Free, no account: https://killercatfish.github.io/math-review-builder/

Real example (Algebra 1 exponents test): https://killercatfish.github.io/math-review-builder/example.html

Mods, happy to take this down if it doesn't fit.

For context I'm In highschool right now and have a test in 2 weeks. I get pretty stressed whenever tests come up especially since last year I barley passed.

I am relatively OK at algebra, I dont struggle but I'm not outstanding. Geometry though is a different story.

I've always been pretty bad at geometry. Every since the 8th grade I've struggled.

Remembering all of these rules and sentences about each shape Isn't the easiest.

I'm starting to think of having to get a private teacher/tutor (whichever you call it) because I notice a lot of the times when I am in the lesson and the teacher explains it I understand what's going on to an extent, but when I get home and try to do the homework I don't even know where to start.

If you could suggest anything I should be doing right now while I have the time to, I would appreciate it.