Please show us what you've tried.
For any real numbers a,b,c & d such that c & d are not both zero, the formula f(x)=(ax+b)/(cx+d) defines a real function.
a)find the domain & range of f.
b)Show that f is a one-to-one function if and only if ad-bc not=0
c)Show that if f is one-to-one, then f' is given by f-1(x)=(dx-b)/(-cx+a) where c & a are both not zero
d) show that if f is one-to-one and a=-d then f-1=f