# Finding Domain without a calculator

• July 29th 2010, 09:05 PM
danielh9103
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.
• July 29th 2010, 09:11 PM
undefined
Quote:

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.
• July 29th 2010, 09:14 PM
pickslides
You are on the right track $x^2-4\neq 0$ and $4x-3>0$