Checkpoint: Verifying Inverses Solution

Verify that the given functions are inverses of one another using $f (0) .$ Explain.

$f (x) = \frac{x - 4}{x + 2}$

$f (0) = \frac{0 - 4}{0 + 2} = - \frac{4}{2} f (0) = - 2$

$g (x) = \frac{2 x + 4}{1 - x}$

$g (- 2) = \frac{2 (- 2) + 4}{1 - (- 2)} = \frac{0}{3} g (- 2) = 0$

The functions are inverses of one another by definition because $f (0) = - 2$ and $g (- 2) = 0 .$

Note

Q: If an ordered pair in $f (x)$ is (4, 0) what will it be in its inverse $g (x)$ ?
A: (0, 4)

Remember that you must find the answer to $f (0)$ because it is the value that is substituted into $g (x) .$