# Thread: Finding Domain without a calculator

1. ## Finding Domain without a calculator

I know the answer is (0,2) U (2, infinity)

f(x) = squareroot(4x-3)
(x^2)-4

Do you set the denominator to zero? I am not 100% sure.

2. Originally Posted by danielh9103
I know the answer is (0,2) U (2, infinity)

f(x) = squareroot(4x-3)
(x^2)-4

Do you set the denominator to zero? I am not 100% sure.
$\displaystyle f(x) = \frac{\sqrt{4x-3}}{x^2-4}$

Are you sure it's not $\displaystyle \left[\frac{3}{4},2\right)\cup (2,\infty)$?

You are on the right track; set the denominator to zero because when it is zero, f is undefined (so exclude any such x from the domain). Also, solve $4x-3<0$ because that will make $\sqrt{4x-3}$ non-real.

3. You are on the right track $x^2-4\neq 0$ and $4x-3>0$