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johnny101
 2 years ago
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johnny101
 2 years ago
1

This Question is Closed

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

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2What 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.

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

jdoe0001
 2 years ago
Best ResponseYou've already chosen the best response.0hmmm if you complete the square on the inverse, I do get an inverse function

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2Can you demonstrate that?

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

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2Johnny.......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".

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

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2Johnny...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.

jdoe0001
 2 years ago
Best ResponseYou've already chosen the best response.0ahemm, 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

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2But, 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.

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2Its inverse will be + sqrt(x)

johnny101
 2 years ago
Best ResponseYou've already chosen the best response.0so 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?

jdoe0001
 2 years ago
Best ResponseYou've already chosen the best response.0notice the picture, the "red inverse" would not pass the vertical line test

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2I 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.

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2Why not ask your teacher?

johnny101
 2 years ago
Best ResponseYou've already chosen the best response.01 quick question, does it matter if its f(x) = x^22x or f(y)= x^22x?

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

Easyaspi314
 2 years ago
Best ResponseYou've already chosen the best response.2Again, 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.

jdoe0001
 2 years ago
Best 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 \(\bf function\)
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