Decide if the function f(x)=(x-1)/(7x-3) may be invertible?

A function is invertible if and only if is a
bijection.

We'll check if for the given function there is
an inverse function.

We'll inter-change x and y and we'll
get:

x =  (y-1)/(7y-3)

Now,
we'll multiply both sides by 7y-3:

x(7y - 3) = y -
1

We'll remove the
brackets:

7xy - 3x = y -
1

We'll keep all the terms in y to the left side, the rest
of term being moved to the right side.

7xy - y = 3x -
1

We'll factorize by y to the left
side:

y(7x - 1) = 3x - 1

We'll
divide by 7x - 1

y = (3x - 1)/(7x -
1)

There is an inverse function and this one
is: f^-1(x) = (3x - 1)/(7x - 1)