Question

For what values of x is ((log(3-x)/(sqrt(x-1)) defined?

Answer 1

Answer: 1<x<3

Explanation:

There are 3 rules in one that are needed for this problem

1st: you can never get a 0 at the bottom of a denominator so x
`\\eq` 1

`√(x-1)=0\\ x-1=0\\x=1` would make a value of 0 on the bottom of a denominator which is not allowed.

2nd: you can never get a - under the square root so x cannot be less than 1

3rd. you can never get a log that is equal to 0 or less than 0 so x

3-x=0

-x=-3

x=3

so x cannot =3 or be greater than 3

the values that x CAN be are 1<x<3