Linear Algebra Examples

$y = \log_{4} (4 x^{3} - x + 1)$

Step 1

Set the argument in $\log_{4} (4 x^{3} - x + 1)$ greater than $0$ to find where the expression is defined.

$4 x^{3} - x + 1 > 0$

Step 2

Solve for $x$ .

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Step 2.1

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 0.76068985$

Step 2.2

The solution consists of all of the true intervals.

$x > - 0.76068985$

Step 3

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

Interval Notation:

$(- 0.76068985, \infty)$

Set-Builder Notation:

${x | x > - 0.76068985}$

Step 4