​ Let f : R - {-4/3} → R be a function defined by f(x) = ​4x/3x + 4, x ≠ -4/3

Question

Let f : R - {\({\frac{-4}{3}}\)} → R be a function defined by f(x) = \(\frac{4x}{3x + 4}, x ≠ \frac{-4}{3}\).

show that f^-1(y) = \(\frac{4y}{4-3y}\)

Answer 1

Given;

  f : R - {\({\frac{-4}{3}}\)} → R and f(x) = \(\frac{4x}{3x + 4}\)

Let g(y) = \(\frac{4y}{4-3y}\)