Show f1 is bijective Let f X rightarrow Y be an invertible f

Show f^-1 is bijective

Let f: X rightarrow Y be an invertible function and let f_-1 : y rightarrow x denote the inverse of f. show that f_-1 is bijective and that f is the inverse of f_-1

Solution

given f is invertible => f is bijective => f is one - one and onto

for given y you can find unique x

=.> for given x you can find unique y

hence f^-1 is one - one and onto

f is bijective