Inverse of a complex function

hi, i have been set the following problem, where z is a complex number:

What is the domain of the function f(z) = (3z+1)/(z+i) ?

Prove that f, defined in the domain of f, has an inverse function (f-1),

i.e. check all necessary properties for the existence of an inverse function.

Determine f-1 and its domain.

I have managed to find the domain and image of the function, and therefore the domain of f-1,

but the problem im having is showing that the function is 1-1 (or injective), in order to show that it has an inverse.

any help would be greatly appreciated!

Re: Inverse of a complex function

Straight algebra and the definition works:

Re: Inverse of a complex function

This message looks very similar to the coursework I set my Complex Analysis class. Paul please come see me in my office when I return. This is a clear violation of the academic code of conduct.