The above function is given:

Question

f(x)= sqrt of (2x-6)/(x-8)

- Sarah describes the domain as [3, ∞).
- Describe why her domain is incorrect.
- Provide the correct domain for the function.

(I sort of understand this).

Answer 1

Sarah is correct in concluding that the domain of √(2x-3) is [3, ∞). But

x-8 = 0 when x=8
division by zero is not defined
8 is not in the domain, so [3, ∞) cannot be the domain, since it includes 8.

So, what is the domain?

Answer 2

I think the domain would be (-∞, 7].
I am not sure if it is correct. I got the above part correct though.

Answer 3

No, the domain is

[3,8)U(8,∞)