Find the Inverse of a Function | Step-by-Step Guide & Examples

[danago]

Hi. The question wants me to find the inverse of $$y = \frac{{x - 1}}{{x - 2}}$$

Heres my working for it:
$$\begin{array}{l}<br /> x = \frac{{y - 1}}{{y - 2}} \\ <br /> xy - 2x = y - 1 \\ <br /> xy - y = 2x - 1 \\ <br /> (x - 1)y = 2x - 1 \\ <br /> y = \frac{{2x - 1}}{{x - 1}} \\ <br /> \end{array}$$

The answer says something different though.

If anybody could please tell me where I am going wrong, or perhaps if the answer book is wrong, id greatly appreciate it.

Thanks,
Dan.

 

[danago]

Ahh nevermind sorry.

My stupid mistake. The answer said $$y = \frac{{1 - 2x}}{{1 - x}}$$ which i just realized is exactly the same thing.

Thanks anyway :)