Question

How do you find the domain of the function: `g(x)=3/(10-3x)`?

Answer 1

The domain of `g(x) = 3/(10 - 3x` is `x != 10/3`.

Explanation:

THe domain of any function is the set of all the values which can be used for the input variable, which is `x`. The domain is All Real Numbers unless tere is an `x` in a denominator of a fraction or in a radicand of a root with an even index.

If there is an `x` in a denominator, to determine the restrictions on the domain, set the expression from the denominator equal to `0` and solve for `x`. The solution(s) obtained willl be the values which cannot be included in the domain.

If there is an `x` in a radicand of a root with an even index, set the expression from the radicand less than `0` and solve for `x`. The solution range obtained cannot be included in the domain.
This is how to find the domain for this function:

`g(x) = 3/(10 - 3x)`

`10 - 3x = 0`
`10 - 10 - 3x = 0 - 10`
`-3x = -10`
`(-3x)/3 = (-10)/-3`
`x = 10/3`

The domain of the function is `x != 10/3`.

In set-builder notation, this is written `D = {x|x != 10/3}`.