Answer
$f(x)=|x-1|\sqrt{3}$
Work Step by Step
Factor out 3 in the trinomial to obtain:
$f(x)=\sqrt{3(x^2-2x+1)}$
The trinomial is a perfect square whose factored form is $(x-1)^2$.
Thus,
$f(x)=\sqrt{3(x-1)^2}$
The principal square root of any number/expression is always non-negative.
Since $x$ can be any real number, then an absolute value must be applied to the principal square root of $(x-1)^2$ to make it non-negative for all values of $x$.
Thus, simplifying the function gives:
$f(x)=\sqrt{3(x-1)^2}
\\f(x)=|x-1|\sqrt{3}$
