Question

Let f : R – (- $\frac{4}{3}$) → R be a function, defined as f(x) = $\frac{4x}{3x+4}$, x ≠ – $\frac{4}{5}$.

The inverse off is map g: Range f → R – is given by $\frac{4}{3}$ is given by

(A) g(y) = $\frac{3y}{3-4y}$

(B) g(y) = $\frac{4y}{4-3y}$

(C) g(y) = $\frac{4y}{3-4y}$

(D) g(y) = $\frac{3y}{4-3y}$

Answer 1

f : R – {$\frac{-4}{3}$} → R is a function defined by f(x) = $\frac{4x}{3x+4}$

Let y = $\frac{4x}{3x+4}$.

⇒ 3xy + 4y = 4x

or x(4 – 3y) = 4y

∴ x = $\frac{4y}{4-3y}$

∴ f-1(4y) = g(y) = $\frac{4y}{4-3y}$

So, part (B) is the correct answer.