1. ## Domains

find the domain.
1. f(x)= x/ (3x-2)

2. In question 1 your denominator cannot not equal zero.

Therefore solve for $\displaystyle 3x-2 = 0$ Domain will be all real numbers apart from the number found from this equation.

In question 2 the number inside the radical must be positive so solve for $\displaystyle 3-x >0$ also $\displaystyle x>0$ After you have solved these 2 the intersection of these sets will be the domain.

3. Originally Posted by pickslides
In question 1 your denominator cannot not equal zero.

Therefore solve for $\displaystyle 3x-2 = 0$ Domain will be all real numbers apart from the number found from this equation.

In question 2 the number inside the radical must be positive so solve for $\displaystyle 3-x >0$ also $\displaystyle x>0$ After you have solved these 2 the intersection of these sets will be the domain.
thankyou! i'm still kinda confused though. can you put it in the most simple terms?
i solved for 3x-2=0 and got x=2/3.
now where does infinity come in?

4. The domain is the set of numbers that the function is defined over.

You have found that $\displaystyle x \neq \frac{2}{3}$ that is great. Where does infinity come in? Well every other number can be found in the domain of the function so we use infinity helps us describe this. We say the domain is all numbers from negative infinity to infinity except $\displaystyle x \neq \frac{2}{3}$

Does this make sense?

The notation we use is $\displaystyle \mathbb{R}/({\frac{2}{3}})$

This means all real numbers apart from 2/3