Find the domain of the following function

Question

g(x)=frac  sqrt{x-3}/{5-x}  write your answer in interval notation

 

so it basically looks like this

g(x)= sqrt x-3

          ----------

          5-x

 

( imagine thats a fraction)   I would really appreciate some help, im having serious difficulty with it...thank you so much!

Answer 1

Domain = possible x values

x can't be < 3 because that would mean we're trying to take the sqrt of a negative number.

x can't be 5 because that would make the bottom of the fraction 0.

[3,Infinity), x not = 5.

.

(I don't know how to express punching out a single value (x=5) in interval notation)