Precalculus Examples

$f (x) = 8 x^{\frac{1}{4}}$

Step 1

Find the domain to determine if the expression is continuous.

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Step 1.1

Convert expressions with fractional exponents to radicals.

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Step 1.1.1

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$8 \sqrt[4]{x^{1}}$

Step 1.1.2

Anything raised to $1$ is the base itself.

$8 \sqrt[4]{x}$

$8 \sqrt[4]{x}$

Step 1.2

Set the radicand in $\sqrt[4]{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

Step 1.3

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 2

The expression is continuous.

Continuous

Step 3

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$