Find the Domain f(x) = square root of 45-5x

$f (x) = \sqrt{45 - 5 x}$

Step 1

Set the radicand in $\sqrt{45 - 5 x}$ greater than or equal to $0$ to find where the expression is defined.

$45 - 5 x \geq 0$

Step 2

Solve for $x$ .

Subtract $45$ from both sides of the inequality.

$- 5 x \geq - 45$

Divide each term in $- 5 x \geq - 45$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq - 45$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{- 45}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{- 45}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{- 45}{- 5}$

Simplify the right side.

Divide $- 45$ by $- 5$ .

$x \leq 9$

Step 3

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

Interval Notation:

$(- \infty, 9]$

Set-Builder Notation:

${x | x \leq 9}$

Step 4

Find the Domain f(x) = square root of 45-5x

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