# Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises: 55

$f^{-1}(x) = \frac{4x}{1 - x}$

#### Work Step by Step

$f(x) = \frac{x}{x + 4}$ $y = \frac{x}{x + 4}$ y(x + 4) = x yx + 4y = x 4y = x - yx 4y = x(1 - y) $x = \frac{4y}{1 - y}$ $f^{-1}(x) = \frac{4x}{1 - x}$

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