i need help for this question.

Question

Find the domain of the function. (Enter your answer using interval notation.)

k(x) =

x + 5

x − 7

Answer 1

k(x) = (x+5) / (x-7)

We can't divide by 0, so x - 7 ≠ 0. So, x ≠ 7.

Domain: all real numbers except 7. Using interval notation: (-∞,7) ∪ (7, ∞).

Answer 2

This is a rational function, which is always defined except for those x values that make the denominator 0, since dividing by 0 is not a well defined operation.

Domain: x ∈ℜ such that (x-7) ≠ 0 ⇒ ∀x≠7