Question

what is the inverse of the function y=-3

Answer 1

This really isn't a question. If you have a function, its inverse returns the identity function \(f(x)=x\) when you compose the function and the inverse.

There does not exist an \(g(x)\) such that \(y(g(x))=x.\)

Answer 2

If this isn't so tangible, look at what you're working with. \(y=-3\) is the same as \(f(x)=-3.\) Is there anything which you can "put inside" the \((x)\) part to return \(x\)? No. Why? Everything you put in the \((x)\) part returns \(-3.\) e.g. \(f(1)=-3\), \(f(2)=-3\), \(f(3)=-3\), \(f(31512580914)=-3\), \(f(\phi)=-3\), \(f(e)=-3\), \(f(\pi)=-3\),. . . .

Answer 3

well i didnt come up with the problem...its a multiple choice problem and i have to graph the function and its inverse

Answer 4

There's a typo in the system, then. @KingGeorge, wouldn't you agree with what I've stated?

Answer 5

I'm going to assume that the method you're supposed to use to find the inverse is simply to replace every \(y\) with an \(x\) and every \(x\) with a \(y\). Hence, the inverse would be \(x=-3\).

In other words, this reflects over the \(y=x\) line.

Answer 6

In a more advanced sense, @Limitless is completely correct. This function doesn't really have an inverse. However, at the level your other questions seem to be at, replacing \(y\) with \(x\) and vice versa is probably what your teacher is expecting.

Answer 7

This is somewhat tangential. But, I don't like the way this problem gives a student an incorrect impression of what an inverse is. It would be nice if these problems did not exist.

Answer 8

What are your thoughts, KG?

Answer 9

Speaking as a math major, I don't like what this problem implies about teaching students inverses either. Speaking as a previous student struggling with the same topic, I would not have understood it if we started discussing the intricacies of what an inverse actually was.

Answer 10

lol thanks for your help guys! ill be sure to tell my teacher about your opinions:)

Answer 11

You're welcome. Just be very very polite. Teachers are sometimes easily offended. :P