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:
$$\begin{array}{l} x = \frac{{y - 1}}{{y - 2}} \\ xy - 2x = y - 1 \\ xy - y = 2x - 1 \\ (x - 1)y = 2x - 1 \\ y = \frac{{2x - 1}}{{x - 1}} \\ \end{array}$$

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 :)

 

[Architeuthis Dux]

Hello Dan,

Thank you for your question. Your steps for finding the inverse of the function y = \frac{{x - 1}}{{x - 2}} are correct. However, the answer given in the guide is also correct. It is a common practice to simplify the final answer by factoring out any common factors. In this case, the expression (x - 1) can be factored out from the numerator, giving us the final answer of y = \frac{2}{x - 1}. Both answers are mathematically equivalent and can be used interchangeably.

I hope this clarifies the issue for you. Keep up the good work in your studies!

Best,