Find the Domain f(x) = square root of 40-4x

$f (x) = \sqrt{40 - 4 x}$

Step 1

Set the radicand in $\sqrt{40 - 4 x}$ greater than or equal to $0$ to find where the expression is defined.

$40 - 4 x \geq 0$

Step 2

Solve for $x$ .

Subtract $40$ from both sides of the inequality.

$- 4 x \geq - 40$

Divide each term in $- 4 x \geq - 40$ by $- 4$ and simplify.

Divide each term in $- 4 x \geq - 40$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \leq \frac{- 40}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \leq \frac{- 40}{- 4}$

Divide $x$ by $1$ .

$x \leq \frac{- 40}{- 4}$

Simplify the right side.

Divide $- 40$ by $- 4$ .

$x \leq 10$

Step 3

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

Interval Notation:

$(- \infty, 10]$

Set-Builder Notation:

${x | x \leq 10}$

Step 4

Find the Domain f(x) = square root of 40-4x

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