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Exercises Functions

Example 7 from Algebra and Trigonometry, 3.7 Inverse Functions

Inverting the Fahrenheit-to-Celsius Function

Find a formula for the inverse function that gives Fahrenheit temperature as a function of Celsius temperature.

C = \frac{5}{9} (F - 32)

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
$\begin{matrix} C & = & \frac{5}{9} (F - 32) \\ C \cdot \frac{9}{5} & = & F - 32 \\ F & = & \frac{9}{5} C + 32 \end{matrix}$

By solving in general, we have uncovered the inverse function. If

$y$

then

$F = h^{- 1} (C) = \frac{9}{5} C + 32$
In this case, we introduced a function $h$ to represent the conversion because the input and output variables are descriptive, and writing $C^{- 1}$ could get confusing.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve for $x$ in terms of $y$ given $y = \frac{1}{3} (x - 5) .$

How did it go?

PreviousEvaluating a Function and Its Inverse from a Graph at Specific Points Next Solving to Find an Inverse Function

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.