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johnny101
1
As you are correct, x^2 - 2x has no inverse. BUT, if you restrict the domain, it would have an inverse.
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.
Ok thankyou that's what I thought, its a multiplce choice homework but I was confused because it can and cant have one
hmmm if you complete the square on the inverse, I do get an inverse function
Can you demonstrate that?
x^2-x2 is a parabola graph therefore passes vertical line test and has inverse?
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".
so the question is determine if the function have an inverse f^-1, so in that regards it does? Now im confused
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.
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
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.
Its inverse will be + sqrt(x)
so for the sake of a multiple choice homework, worded does it contain the function f^-1, x^2-2x does not because it then becomes a horizontal parabola i.e failing the vertical line test?
notice the picture, the "red inverse" would not pass the vertical line test
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.
Why not ask your teacher?
1 quick question, does it matter if its f(x) = x^2-2x or f(y)= x^2-2x?
\(\bf y = x^2-2x\qquad inverse\implies x = y^2-2y\\ \quad \\ x = y^2-2y+1-1\implies x = (y-1)^2-1\implies \sqrt{x+1}+1=y\)
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.
@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 \(\bf function\)