x^2/4x-3 what is the domain. I can figure this out

Question

This equation has me stumped, I know that it can not equal zero but that is it. Please help.

Answer 1

x²/(4x-3)

 

The domain is all possible input values for x

The only restriction is that we cannot divide by zero so

set 4x-3=0 and solve to find the restriction..

 

4x-3 = 0    add 3 to both sides

4x=3         divide both sides by 4

x = 3/4

 

The only restriction is x cannot equal 3/4 or .75

 

In interval notation this is:  (-∞, 3/4)U(3/4, ∞)

 

The open parentheses denote that the value 3/4 and ∞ are not included.

If you are more comfortable with showing the domain as an inequality

we have:

 

[-∞ < x <3/4] U [3/4 < x < ∞]