How can I set a domain of all the real numbers except a particular number in Geogebra?

Pablo shared this question 5 months ago

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So I want to find the inverse of e(x) = x / (-x + 2). This function has all the real numbers except 2, where is undefined. What I tried to do was to do an if-statement saying (if x != 2, x / (-x +2)), but it stills give me undefined. Is there a way to plug the domain of this function? Without this value it should have indeed an inverse.

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Best Answer

Michael Borcherds ● 5 months ago

OK, try this

If(x != 2 && x!=-1, x / (-x +2))

f(x) = If(x ≠ 2 ∧ x ≠ -1, x / (-x + 2))

Comments (7)

Pablo ● 5 months ago

I also didn't notice that this function is restricted on -1, as the inverse would be undefined. So, it would be cool to know about a way to have the domain as all the real numbers except these last two.

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Simona Riva ● 5 months ago

There are restrictions on the use of Invert( ) command for functions.

Please see the wiki. https://wiki.geogebra.org/e...

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Pablo ● 5 months ago

Hello Simona, thank you for your response and thank you for your wok on Geogebra specifically and to the society in general (as you also write math textbooks). I know there are restrictions on the Invert function (that's why I'm not using it). As the wiki well says I cannot determine the domain. Furthermore, for a function with more than an x, another option might be more suitable.

As I state on my OP, I'm using a conditional for setting this domain but I need to restrict another value (-1) for not getting the inverse undefined. What option would you recommend me for solving my problem? I can share my work if I'm not explaining myself correctly enough.

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Michael Borcherds ● 5 months ago

Do you mean like this?

if(x != 2, x / (-x +2))

If not please explain

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Pablo ● 5 months ago

No, now doing the math I've seen that -1 is already not included in the domain of the original function, we just have to restrict that 2. But imagine we have to restrict another value in any other equation. Is there a way where I can do that same if statement but for more values?

Would be correct (moreover optimal) to do:

if(x != 2, x/ (-x +2), x!= 0, x / (-x + 2))

? I guess that's the answer; mutliple if statements in order to restrict some values.

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Michael Borcherds ● 5 months ago

OK, try this

If(x != 2 && x!=-1, x / (-x +2))

f(x) = If(x ≠ 2 ∧ x ≠ -1, x / (-x + 2))

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Pablo ● 5 months ago

Thank you very much. How can I close the thread? Like I see it puts still needs answer, although I've posted your answer as the best answer. I don't know if the thread closes automatically or something due to inactivity in a certain period of time. Have a nice day.

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