# Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 263: 48

Therefore f and g are inverses of each other

#### Work Step by Step

$f(x) = \frac{x - 5}{3x + 4}$ Find the inverse $y = \frac{x - 5}{3x + 4}$ y(3x + 4) = x - 5 3xy + 4y = x - 5 4y + 5 = x - 3xy 4y + 5 = x(1 - 3y) $\frac{4y + 5}{1 - 3y} = x$ $f^{-1}(x) = \frac{4x + 5}{1 - 3x}$ = g(x) $g(x) = \frac{5 + 4x}{1 - 3x}$ Find the inverse $y = \frac{5 + 4x}{1 - 3x}$ y(1 - 3x) = 5 + 4x y - 3xy = 5 + 4x y - 5 = 4x + 3xy y - 5 = x(4 + 3y) $\frac{y - 5}{4 + 3y} = x$ $g^{-1}(x) = \frac{x - 5}{4 + 3x}$ = f(x) Therefore f and g are inverses of each other

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