Precalculus Examples

$\ln (2 - x)$

Set the argument in $\ln (2 - x)$ greater than $0$ to find where the expression is defined.

$2 - x > 0$

Solve for $x$ .

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Subtract $2$ from both sides of the inequality.

$- x > - 2$

Divide each term in $- x > - 2$ by $- 1$ and simplify.

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Divide each term in $- x > - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{- 2}{- 1}$

Simplify the left side.

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Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x < \frac{- 2}{- 1}$

Simplify the right side.

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Divide $- 2$ by $- 1$ .

$x < 2$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 2)$

Set-Builder Notation:

${x | x < 2}$