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Exercises Functions

Example 8 from Algebra and Trigonometry, 3.7 Inverse Functions

Solving to Find an Inverse Function

Find the inverse of the function $f (x) = \frac{2}{x - 3} + 4.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\begin{matrix} y & = & \frac{2}{x - 3} + 4 & Set up an equation . \\ y - 4 & = & \frac{2}{x - 3} & Subtract 4 from both sides . \\ x - 3 & = & \frac{2}{y - 4} & Multiply both sides by x - 3 and divide by y - 4. \\ x & = & \frac{2}{y - 4} + 3 & Add 3 to both sides . \end{matrix}$
So $f^{- 1} (y) = \frac{2}{y - 4} + 3$ or $f^{- 1} (x) = \frac{2}{x - 4} + 3.$

How did it go?

PreviousInverting the Fahrenheit-to-Celsius Function Next Solving to Find an Inverse with Radicals

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.