Intermediate Algebra for College Students (7th Edition)

$f(x) = 6|x+2|$
Write 36 as $6^2$, and then simplify to obtain: $f(x)=\sqrt{6^2(x+2)^2} \\f(x)=6\sqrt{(x+2)^2}$ 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 $f(x)=6\sqrt{(x+2)^2}$, rule (ii) above must be used. Therefore, $f(x) = 6|x+2|$