Question

1

Answer 1

As you are correct, x^2 - 2x has no inverse. BUT, if you restrict the domain, it would have an inverse.

Answer 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.

Answer 3

Ok thankyou that's what I thought, its a multiplce choice homework but I was confused because it can and cant have one

Answer 4

hmmm if you complete the square on the inverse, I do get an inverse function

Answer 5

Can you demonstrate that?

Answer 6

one sec

Answer 7

x^2-x2 is a parabola graph therefore passes vertical line test and has inverse?

Answer 8

2x*

Answer 9

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".

Answer 10

so the question is determine if the function have an inverse f^-1, so in that regards it does? Now im confused

Answer 11

hmmm

Answer 12

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.

Answer 13

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

Answer 14

Agree...

Answer 15

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.

Answer 16

Its inverse will be + sqrt(x)

Answer 17

@johnny101 http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjItMngiLCJjb2xvciI6IiMzMzE1QUQifSx7InR5cGUiOjAsImVxIjoic3FydCh4KzEpKzEiLCJjb2xvciI6IiNFQjQ5NTYifSx7InR5cGUiOjAsImVxIjoiLXNxcnQoeCsxKSsxIiwiY29sb3IiOiIjQzkwQTBBIn0seyJ0eXBlIjoxMDAwfV0-

Answer 18

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?

Answer 19

notice the picture, the "red inverse" would not pass the vertical line test

Answer 20

thanks!

Answer 21

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.

Answer 22

Why not ask your teacher?

Answer 23

1 quick question, does it matter if its f(x) = x^2-2x or f(y)= x^2-2x?

Answer 24

\(\bf y = x^2-2x\qquad inverse\implies x = y^2-2y\\ \quad \\
x = y^2-2y+1-1\implies x = (y-1)^2-1\implies \sqrt{x+1}+1=y\)

Answer 25

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.

Answer 26

@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 \(\bf function\)

Answer 27

alright understood