Solving for x: Are F(x) and G(x) Equivalent?

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Homework Help Overview

The discussion revolves around the equivalence of two functions, F(x) and G(x), specifically examining whether they are equivalent given the potential restrictions on their domains. The subject area includes algebra and function analysis.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the simplification of F(x) and question the implications of dividing by zero. There are inquiries about the definitions and domains of both functions, particularly at x=1, and whether the lack of explicit domain information affects their equivalence.

Discussion Status

The discussion is active, with participants raising important questions about the definitions and domains of the functions. Some guidance is offered regarding the implications of domain restrictions, but no consensus has been reached on the equivalence of F(x) and G(x).

Contextual Notes

There is uncertainty regarding the domains of the functions, as the original problem does not specify them. Participants are considering the implications of this lack of information on the equivalence of the functions.

brycenrg
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F(x) = (x^2 - x)/(x-1)
G(x)= x

I factored x^2-x and canceled denominator of f(x) which simplify to x

So it does equal x does not now matter that in original equation x cannot = 1 otherwise denominator = 0

I'm just making sure they are = and but maybe not equivalent. Trying to learn more of maths. Thank you.
 
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Is F(x) defined when x=1? Is G(x) defined there?

ehild
 
The problem doesn't say
 
Can you divide by zero? ehild
 
No but you can manipulate the equation to be x.
 
You manipulated it by dividing with an expression that can be zero. It is forbidden.
Try to input (1^2-1)/(1-1) in your calculator . What does it say? :-p


ehild
 
Do F and G have the same domains?
 
brycenrg said:
The problem doesn't say

If it doesn't state the domains then, strictly speaking, it is impossible to say whether the functions are equal. I can claim the functions f = x and g = 2x are equal if the domain is {0}. Conversely, f = x and g = x are different functions if I specify different domains.

If no value is specified for F(1), is 1 in F's domain?
Consider whether 1 might be in G's domain, and the consequences.
 
brycenrg said:
The problem doesn't say
It might be that the domains are implied - that is, the domain for each function might be the real numbers for which each function is defined. It might be that this is actually stated in the problem and you didn't include it in the problem description.

If there actually isn't any information given in the problem, what would be the implied domains for F and G?
 

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