Given, f(x)=(2x+3)/(4x+5) for x≠-5/4; f^-1(x)=?

Answer 1

This problem can be solved using the standard algorithm.

y = (2x +3) /(4x+5) interchange x and y

x = (2y +3) / ( 4 y +5) then solve for y

y = (3-5x) / (-2 + 4 x)

So f^-1 (x) = (3 - 5x) /(-2 + 4 x)

Notice that the original vertical asymptote has become a horizontal asymptote at y = -5/4

Also the original horizontal asymptote is now a vertical asymptote at x = -1/2