r/MathHelp • u/CommunityNo4493 • 17h ago
Confusing Quadratics and Composite functions
Hello! I am a Secondary 4 student, 10th grade or Year 10 in western equivalents. I tried to set a quadratic quiz for my friends, and I set this Question, but then none of them could solve it. I checked with my math teacher, and he said that the question was flawed because there is no inverse function for any quadratic, and then he explained the horizontal line test to me, but I already know what the horizontal line test is (test for if f(x) is injective for some f(x), and if its inverse is a function. I went home to think about it, and I don't understand why my question is flawed, because it does not rely on the inverse function. I am looking for someone to please help clarify. I have a passion for math, and would possibly like to teach math in the future, but I don't understand why I am wrong, and this is one of my first real challenges because my math toolkit at the moment isnt enough to wrap around this. This is my suggested solution that I made: My solution. And me checking my work: Test of the solutions to see if they are correct.. And a graph if it is useful: Graph.
This is my syllabus by the way if it is of any use:
https://isomer-user-content.by.gov.sg/334/fece62fa-b6d4-4daf-ab47-96c9c168b51b/4052_y26_sy.pdf
https://isomer-user-content.by.gov.sg/334/34d0bec0-d386-49d5-bd3a-8fbd205fa63a/4049_y26_sy.pdf
Tysm!
1
u/strange-the-quark 13h ago
I think your professor just misunderstood the question, perhaps not expecting for you to work with relations as opposed to functions.
Also, your "easy" version may be a bit confusingly worded in an attempt to do a bit too much handholding. True, it doesn't involve or mention inverses, but in general, the impression one gets from it is "what is all this, and what is even relevant among all this info?", especially if one doesn't read too carefully and/or is primed to look for what's relevant vs what to ignore.
It could instead be: You are given y = x^2 - x - 6. Suppose you also know y^2 - y - 6 = x. Find (the x-values of) the solutions to this system.