f(x)= (4x-1)/2x+3

To find the inverse function f(x)^-1 we will assume:

y=(4x-1)/(2x+3)

==> multiply by 2x+3

==> y(2x+3)= 4x-1

==> 2yx+3y=4x-1

==> 3y+1= 4x-2yx

==> 3y+1= x(4-2y)

==> x= (3y+1)/(4-2y)

==> f(x)^-1= (3x+1)/(4-2x)

f(x)= (4x-1)/2x+3

To find the inverse function f(x)^-1 we will assume:

y=(4x-1)/(2x+3)

==> multiply by 2x+3

==> y(2x+3)= 4x-1

==> 2yx+3y=4x-1

==> 3y+1= 4x-2yx

==> 3y+1= x(4-2y)

==> x= (3y+1)/(4-2y)

==> f(x)^-1= (3x+1)/(4-2x)