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

Apr 15, 2018

The domain of g(x) = 3/(10 - 3x is $x \ne \frac{10}{3}$.

#### 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:

$g \left(x\right) = \frac{3}{10 - 3 x}$

$10 - 3 x = 0$
$10 - 10 - 3 x = 0 - 10$
$- 3 x = - 10$
$\frac{- 3 x}{3} = \frac{- 10}{-} 3$
$x = \frac{10}{3}$

The domain of the function is $x \ne \frac{10}{3}$.

In set-builder notation, this is written $D = \left\{x | x \ne \frac{10}{3}\right\}$.