Thread: Inverse/Domain Question

i have this question:

Restrict the domain of the function f(x) = (2x-3)/(x²-x) so that an inverse function exists. Find the range and domain.

I've tried to find the inverse of this function, but have found it difficult to make x the subject. Any suggestions?

Sketch the graph.

Thats it? For all other questions it has been specified when i should solve graphically, this time it hasn't, so i have presumed he wants it to be solved by other means

The question does not ask you for the formula of the inverse function, only for its range and domain. After you sketch the graph of the original function, you may find its critical points, and this may be enough to find the domain and range. Of course, course requirements vary and you may be required to prove that the graph indeed behaves as in your sketch (for example, that the x-axis is the horizontal asymptote).

But I usually sketch the graph anyway, if only to understand what I am supposed to prove next.