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Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
As you are correct, x^2  2x has no inverse. BUT, if you restrict the domain, it would have an inverse.
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
What we mean "it has no inverse"...that when you find the inverse, it will not be a function. So we say it has no inverse.
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
Ok thankyou that's what I thought, its a multiplce choice homework but I was confused because it can and cant have one
 11 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.0
hmmm if you complete the square on the inverse, I do get an inverse function
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
Can you demonstrate that?
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
x^2x2 is a parabola graph therefore passes vertical line test and has inverse?
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
Johnny.......you can find the inverse of x^2  2...no one is doubting that...but the inverse will not be a function..we call that the function not being "invertible".
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
so the question is determine if the function have an inverse f^1, so in that regards it does? Now im confused
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
Johnny...that language is a very touchy area...many textbooks say that it does not have an inverse.....other textbooks say it has an inverse, whose inverse is not a function. It really is a question of symmantics. So a question has to worded very carefully to accomodate the many texts out there.
 11 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.0
ahemm, I see.... the inverse expression I should call it, will not meet the criterion of a "function" since it'd be a horizontal parabola and thus not a function that will pass the vertical line test
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
Agree...
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
But, everyone will agree that if we have a function f(x) = x^2 , and we restrict the domain to the positive real numbers, then the function has an inverse, no if's and's or but's.
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
Its inverse will be + sqrt(x)
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
so for the sake of a multiple choice homework, worded does it contain the function f^1, x^22x does not because it then becomes a horizontal parabola i.e failing the vertical line test?
 11 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.0
notice the picture, the "red inverse" would not pass the vertical line test
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
thanks!
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
I prefer not to answer that question as I do not know which textbook you are using and how the author feels about the issue. But, I can tell you, that on a national exam, etc.. such a question would have to be worded so carefully as to accomodate all textbboks.
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
Why not ask your teacher?
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
1 quick question, does it matter if its f(x) = x^22x or f(y)= x^22x?
 11 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.0
\(\bf y = x^22x\qquad inverse\implies x = y^22y\\ \quad \\ x = y^22y+11\implies x = (y1)^21\implies \sqrt{x+1}+1=y\)
 11 months ago

Easyaspi314 Group TitleBest ResponseYou've already chosen the best response.2
Again, thats a touchy matter...so I prefer to stay away from there; I dont want to mislead you, as I dont know your teachers' preferences, books style, etc.
 11 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.0
@johnny101 so though you can simplify it and solve for "y", the resulting expression doesn't not meet the criterion of a "function", thus is not a function per se, thus no inverse \(\bf function\)
 11 months ago

johnny101 Group TitleBest ResponseYou've already chosen the best response.0
alright understood
 11 months ago
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