Find a formula for the inverse of the function f=(4x-1)/(2x+3)

Any function f(x) and its inverse function `f^-1(x)` follow the relation `f(f^-1(x)) = x` .

For the function `f(x)=(4x-1)/(2x+3)` , to determine the inverse, use the relation provided earlier. This gives:

`f(f^-1(x)) = x`

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

`(4*(f^-1(x))-1)=x*(2*(f^-1(x))+3)`

`4*f^-1(x) - 2*x*f^-1(x) = 3x + 1`

`f^-1(x)*(4 - 2x) = (3x + 1)`

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

The required inverse of the function `f(x) = (4x-1)/(2x+3)` is` f^-1(x) = (3x + 1)/(4 - 2x)`