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Easyaspi314Best 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.
 5 months ago

Easyaspi314Best 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.
 5 months ago

johnny101Best 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
 5 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
hmmm if you complete the square on the inverse, I do get an inverse function
 5 months ago

Easyaspi314Best ResponseYou've already chosen the best response.2
Can you demonstrate that?
 5 months ago

johnny101Best ResponseYou've already chosen the best response.0
x^2x2 is a parabola graph therefore passes vertical line test and has inverse?
 5 months ago

Easyaspi314Best 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".
 5 months ago

johnny101Best 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
 5 months ago

Easyaspi314Best 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.
 5 months ago

jdoe0001Best 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
 5 months ago

Easyaspi314Best 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.
 5 months ago

Easyaspi314Best ResponseYou've already chosen the best response.2
Its inverse will be + sqrt(x)
 5 months ago

johnny101Best 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?
 5 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
notice the picture, the "red inverse" would not pass the vertical line test
 5 months ago

Easyaspi314Best 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.
 5 months ago

Easyaspi314Best ResponseYou've already chosen the best response.2
Why not ask your teacher?
 5 months ago

johnny101Best 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?
 5 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
\(\bf y = x^22x\qquad inverse\implies x = y^22y\\ \quad \\ x = y^22y+11\implies x = (y1)^21\implies \sqrt{x+1}+1=y\)
 5 months ago

Easyaspi314Best 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.
 5 months ago

jdoe0001Best 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 \(\bf function\)
 5 months ago
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