Question

F(x) = 2x / (x-6) Find the domain of f (all permissible inputs of x)

Answer 1

domain { x : x ∈ R, x ≠ 6 }

Explanation:

given

f(x) =
`(2x)/(x-6)`

the denominator of f(x) cannot be zero as this would make f(x) undefined

Equating the denominator to zero and solving gives the value that x cannot be.

x - 6 = 0 ( add 6 to both sides )

x = 6 ← excluded value in the domain

domain is {x : x ∈ R, x ≠ 6 }