Question

Are this two functions equivalent?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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 \[x \le \frac{ 3 }{ 2 }\]

Answer 5

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

Answer 6

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

Answer 7

So they are equal :)

Answer 8

yup, they are :)