Are this two functions equivalent?

Question

osanseviero · Answer

$$F(x)=\sqrt{4x ^{2}-12x+9}$$ and $$g(x)=\left| 2x-3 \right|$$
There is a restriction for f(x), right?

hartnn · Answer

yes, they both are same 
$\Large |a|=\sqrt{a^2}$

hartnn · Answer

what restriction are you talking about ? 
$\Large (2x-3)^2 \ge 0$
but that is always true , no matter what 'x' is
so, no restriction on x

osanseviero · Answer

So (correct me, please), if I want to know the domain in F(x), it will be x=3/2

Because

$$4x ^{2}-12x+9\ge0$$
So: 
$$x ^{2}-3x+\frac{ 9 }{ 4 }\ge0$$
$$(x-\frac{ 3 }{ 2 })^{2}\ge0$$
So
x$$x \ge \frac{ 3 }{ 2 } $$ or $$x \le \frac{ 3 }{ 2 }$$

osanseviero · Answer

Oh...so the domain in F(x) are all reals! (?)

hartnn · Answer

yes! as (anything)^2 is always >=0

osanseviero · Answer

So they are equal :)

hartnn · Answer

yup, they are :)