## Grazes Group Title Find f^-1(x) and state any restrictions on the domain of f^-1(x) one year ago one year ago

1. Grazes Group Title

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

2. satellite73 Group Title

you need the inverse?

3. Grazes Group Title

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

4. satellite73 Group Title

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 Group Title

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

6. satellite73 Group Title

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

7. satellite73 Group Title

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

8. Grazes Group Title

Okay. I've got it from there

9. Grazes Group Title

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

10. satellite73 Group Title

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 Group Title

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

12. satellite73 Group Title

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

13. Grazes Group Title

Thanks.