You can put this solution on YOUR website! When findind the domain of a function, we must find which values of x work in the equation. In this particular function, there is both a square root sign and an x in the denominator. We must ask ourselves which values of x would create a problem in the function.
We know that there cannot be a negative value under a radical otherwise becomes an imaginary value. So we now now that x must be greater than or equal to 0.
We also know that there cannot be a 0 in the denominator because we cannot divide by 0. For the expression 2x-7, what values of x would make the expression 0? When x=3.5, the expression 2x-7=0. We now know that x cannot equal 3.5.
We must now express the domain in interval notation to incorporate both the restrictions we found out.
D:(0,3.5)U(3.5,infinity)
Incase you are unfamiliar with interval notation, that basically means that x can be anything from 0 to 3.5 (excluding 0 and 3.5) and then be anything from 3.5 to infinity (excluding both values). Hope this helped!
