Answer
$f(x) = |x+1|\sqrt{5}$
Work Step by Step
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 $x \lt -1$, the value of $x+1$ is negative.
Thus, to simplify $f(x)=\sqrt{5(x+1)^2}$, rule (ii) above must be used.
Therefore,
$f(x) = |x+1|\sqrt{5}$
