Checkpoint: Inverses of Functions Algebraically Solution

<strong>Checkpoint: Inverses of Functions Algebraically</strong> Solution

Find the inverse of the function. Check your work.

$q (x) = \frac{9}{2 x - 1}$

$\begin{matrix} y = \frac{9}{2 x - 1} \\ x = \frac{9}{2 y - 1} \\ (2 y - 1) x = \frac{9}{2 y - 1} (2 y - 1) \\ x (2 y - 1) = 9 \\ \frac{x (2 y - 1)}{x} = \frac{9}{x} \\ 2 y - 1 = \frac{9}{x} \\ 2 y = \frac{9}{x} + 1 \end{matrix} y = \frac{1}{2} (\frac{9}{x} + 1) or y = \frac{9}{2 x} + \frac{1}{2}$

$Check when x = 5 q (5) = \frac{9}{2 (5) - 1} = \frac{9}{9} = 1 y = \frac{1}{2} (\frac{9}{1} + 1) = \frac{1}{2} (10) = 5$

Note

Q: What does it mean when you switch the x and y values to find the inverse?
A: The domain and range values of the function are reversed.

Q: Why is it important to check your work when determining the inverse of a function?
A: Sample: Because it uses the definition of a function to check if the inverse was found using $f (a) = b$ and $g (b) = a .$