Find the Domain y(t) = square root of 18-t

$y (t) = \sqrt{18 - t}$

Step 1

Set the radicand in $\sqrt{18 - t}$ greater than or equal to $0$ to find where the expression is defined.

$18 - t \geq 0$

Step 2

Solve for $t$ .

Subtract $18$ from both sides of the inequality.

$- t \geq - 18$

Divide each term in $- t \geq - 18$ by $- 1$ and simplify.

Divide each term in $- t \geq - 18$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- t}{- 1} \leq \frac{- 18}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{t}{1} \leq \frac{- 18}{- 1}$

Divide $t$ by $1$ .

$t \leq \frac{- 18}{- 1}$

Simplify the right side.

Divide $- 18$ by $- 1$ .

$t \leq 18$

Step 3

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

Interval Notation:

$(- \infty, 18]$

Set-Builder Notation:

${t | t \leq 18}$

Step 4

Find the Domain y(t) = square root of 18-t

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