## Grazes 2 years ago Find f^-1(x) and state any restrictions on the domain of f^-1(x)

1. Grazes

$f(x)=\frac{ x }{ x-2 }$ $x \neq 2$

2. satellite73

you need the inverse?

3. Grazes

Yes. I know I need to switch f(x) and x, but I dunno how you would simplify from there

4. satellite73

you can take $y=\frac{x}{x-2}$ switch $$x$$ and $$y$$ to write $x=\frac{y}{y-2}$ and solve for $$y$$

5. satellite73

you get $x=\frac{y}{y-2}$$x(y-2)=y$ as a first step then multiply out

6. satellite73

$xy-2x=y$ put the $$y$$'s on one side of the equal sign, the $$2x$$ on the other $xy-y=2x$

7. satellite73

factor out the $$y$$ on the left $(x-1)y=2x$

8. Grazes

Okay. I've got it from there

9. Grazes

I didn't think to subtract y over ^^;;

10. satellite73

and finally divide the domain will be all real numbers except $$x=1$$ which is not surprising because that was the range of $$f$$

11. satellite73

answer should be $y=\frac{2x}{x-1}$

12. satellite73

yeah you got to get the $$y$$' all on one side good luck

13. Grazes

Thanks.