Finite Math Examples

$\ln (- x^{4} - 1)$

Step 1

Set the argument in $\ln (- x^{4} - 1)$ greater than $0$ to find where the expression is defined.

$- x^{4} - 1 > 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Add $1$ to both sides of the inequality.

$- x^{4} > 1$

Step 2.2

Divide each term in $- x^{4} > 1$ by $- 1$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- x^{4} > 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x^{4}}{- 1} < \frac{1}{- 1}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{4}}{1} < \frac{1}{- 1}$

Step 2.2.2.2

Divide $x^{4}$ by $1$ .

$x^{4} < \frac{1}{- 1}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $1$ by $- 1$ .

$x^{4} < - 1$

Step 2.3

Since the left side has an even power, it is always positive for all real numbers.

No solution

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4