## johnny101 2 years ago 1

1. Easyaspi314

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

2. Easyaspi314

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.

3. johnny101

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

4. jdoe0001

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

5. Easyaspi314

Can you demonstrate that?

6. jdoe0001

one sec

7. johnny101

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

8. johnny101

2x*

9. Easyaspi314

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".

10. johnny101

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

11. jdoe0001

hmmm

12. Easyaspi314

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.

13. jdoe0001

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

14. Easyaspi314

Agree...

15. Easyaspi314

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.

16. Easyaspi314

Its inverse will be + sqrt(x)

17. jdoe0001
18. johnny101

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?

19. jdoe0001

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

20. johnny101

thanks!

21. Easyaspi314

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.

22. Easyaspi314

23. johnny101

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

24. jdoe0001

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

25. Easyaspi314

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.

26. jdoe0001

@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 $$\bf function$$

27. johnny101

alright understood