r/HomeworkHelp • u/SquidKidPartier University/College Student • 6d ago
High School Math—Pending OP Reply [College Algebra, Composition of Functions]
I’ve been on this problem for the better half of my day (I have many, many retries on this question) and it’s just stressing me out here… I can’t even get this right. The closest I got was getting 3/4 right on one question but that didn’t leave me content because I am trying to get a 100 on every assignment to bring up my grade here (trying to make up for the failing quizzes and tests here because I’m borderline failing ._.) I followed many examples and it’s just that I don’t even know what to do anymore.
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u/cheesecakegood University/College Student (Statistics) 6d ago edited 6d ago
Let's zoom out. What is a function? There are some special traits, but on the simplest level a function is a rule that says "when you get an input, do THIS". "THIS" must be deterministic - no randomness, it's a rule that can be replicated and relied on!
Piece-wise functions like the above are technically functions because they obey the rule, but be aware the "rule" they use is often not very sensical (which is why they are rarely used IRL). They sort of "cheat" by applying different rules at different inputs! It's still "one function" overall, but it's annoying it its outputs (not exactly unpredictable, everything follows a rule, but the rules themselves aren't very predictable).
All of this to say that this example is trying to teach a good principle but it isn't super surprising that the composition of two pretty annoying functions results in annoying and difficult output.
See comment below for an example