hi, i have been set the following problem, where z is a complex number:I have managed to find the domain and image of the function, and therefore the domain of f-1,

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.

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!