Question

find the domain of the function f(x) = 2/(8-9x)

Answer 1

R\{8/9}
The bottom cannot be equal to 8/9 or this makes the equation undefined.

Answer 2

f(x) = 2/(8-9x). This function is discontinued for the denominator value =0

 So (8-9x) ≠ 0, or x≠ 8/9

Hence the domain of f(x) =]-∞, 8/9[ ∪ ] 8/9, +∞[
or domain is all real number ≠ 8/9