# How do you find the domain of g(x) = ln(2 - x - x ^2)?

Mar 18, 2018

$- 2 < x < 1$

#### Explanation:

The domain of the function are the values of $x$ that give 1 value for $y$.

For this function, $g \left(x\right)$ is valid when $2 - x - {x}^{2} > 0$

$- \left(x + 2\right) \left(x - 1\right) > 0$

$x + 2 > 0 \mathmr{and} - x + 1 > 0$

$x > - 2 \mathmr{and} x < 1$

$- 2 < x < 1$