Answer
$f(x) = 9|x-2|$
Work Step by Step
Write 81 as $9^2$, and then simplify to obtain:
$f(x)=\sqrt{9^2(x-2)^2}
\\f(x)=9\sqrt{(x-2)^2}$
RECALL:
(i) $\sqrt{a^2} = a$ when $a \ge 0$
(ii) $\sqrt{a^2} = |a|$ when $a \lt 0$
$x$ can be any real number. This means that when $x \lt 2$, the value of $x-2$ is negative.
Thus, to simplify $f(x)=9\sqrt{(x-2)^2}$, rule (ii) above must be used.
Therefore,
$f(x) = 9|x-2|$
