Academic Team Math Practice Test Prep: Practice Exam & Study Guide

To determine the inverse of the function f(x) = \((-12x - 7)/(x + 3)\), we start by letting y be equal to f(x):

\[ y = \frac{-12x - 7}{x + 3} \]

Next, to find the inverse, we switch the roles of y and x, and then solve for y:

\[ x = \frac{-12y - 7}{y + 3} \]

Multiplying both sides by (y + 3) to eliminate the fraction gives:

\[ x(y + 3) = -12y - 7 \]

Expanding the left side results in:

\[ xy + 3x = -12y - 7 \]

Reorganizing the equation to isolate terms containing y on one side yields:

\[ xy + 12y = -7 - 3x \]

Factoring y out from the left side results in:

\[ y(x + 12) = -7 - 3x \]

Finally, dividing both sides by the expression (x + 12) provides the expression for y:

\[ y = \frac{-7 - 3x}{x + 12} \]

This simplifies