The discussion revolves around finding two different functions, f and g, both defined on the set of real numbers, that are equal for all rational inputs. Participants explore the implications of the problem statement and the nature of functions, particularly focusing on piecewise-defined functions.
Participants are actively engaging with the problem, raising questions about the definitions and characteristics of functions. Some have proposed potential function definitions, while others express uncertainty about the problem's context and requirements.
There is mention of the original poster's background in precalculus and their familiarity with piecewise functions, which may influence their understanding of the problem. The discussion also touches on the appropriateness of the problem's placement within the precalculus curriculum.
That is the approach! Define f to be whatever you want, then define g to be that same function on the rationals, but something else on the irrationals. Remember that a "function" does not necessarily mean a single "formula". Such a function cannot be "continuous" anywhere. I do wonder why such a problem would be posted under "precalculus". Since you are the same person who posted the "find f(x) that maps (0, 1) to [0, 1]", what course are these for?L Huyghe said:Homework Statement
Given an example of two different functions f and g, both of which have the set of real numbers as their domain, such that f(x)=g(x) for every rational number.
2. The attempt at a solution
I have yet to figure a way to approach this problem. Since it appears as though they are only equal for rational numbers.
Don't people generally learn the basics of functions in a precalculus class, or earlier?HallsofIvy said:I do wonder why such a problem would be posted under "precalculus".