Question

How do you find the domain of this function `f(x)=1/(3x-6)`?

Answer 1

The only value of `x` for which `f(x) = 1/(3x-6)` is not defined is `x=2` (since this would result in division by zero).

The Domain of `f(x)` is
`(-oo,2)uu(2,+oo)`

Answer 2

Domain `(-oo,2)U(2,oo)`

To find the domain of a function, we first identify the values of x for which f(x) becomes undefined. In the present case, it is observed that if x=2, then f(x) becomes `1/0` or `oo`. Hence the domain would be all real numbers except 2. In interval notation it can be expressed as `(-oo,2)U(2,oo)`. In the set builder notation it would be written as {x:`inR` | x`!in`2}