Find the domain and range of the following function:
$1 - | x - 2 |$

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Solution

$f (x) = 1 - | x - 2 |$
$x \geq 2$
$1 - (x - 2)$
$1 - x + 2$
$3 - x$
$x < 2$
$1 - (2 - x)$
$1 - 2 + x$
$x - 1$
domain $x \in (- \infty, \infty)$

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