Find the Domain y = fourth root of -5x+7

$y = \sqrt[4]{- 5 x + 7}$

Step 1

Set the radicand in $\sqrt[4]{- 5 x + 7}$ greater than or equal to $0$ to find where the expression is defined.

$- 5 x + 7 \geq 0$

Step 2

Solve for $x$ .

Subtract $7$ from both sides of the inequality.

$- 5 x \geq - 7$

Divide each term in $- 5 x \geq - 7$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq - 7$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{- 7}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{- 7}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{- 7}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \leq \frac{7}{5}$

Step 3

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

Interval Notation:

$(- \infty, \frac{7}{5}]$

Set-Builder Notation:

${x | x \leq \frac{7}{5}}$

Step 4

Find the Domain y = fourth root of -5x+7

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