Find the Domain and Range f(x)=-2x^(1/4)

$f (x) = - 2 x^{\frac{1}{4}}$

Step 1

Convert expressions with fractional exponents to radicals.

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

$- 2 \sqrt[4]{x^{1}}$

Anything raised to $1$ is the base itself.

$- 2 \sqrt[4]{x}$

Step 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 3

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, 0]$

Set-Builder Notation:

${y | y \leq 0}$

Step 5

Determine the domain and range.

Domain: $[0, \infty), {x | x \geq 0}$

Range: $(- \infty, 0], {y | y \leq 0}$

Step 6