Calculus Examples

$f (t) = \frac{4}{3 - t}$

Step 1

Set the denominator in $\frac{4}{3 - t}$ equal to $0$ to find where the expression is undefined.

$3 - t = 0$

Step 2

Solve for $t$ .

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Step 2.1

Subtract $3$ from both sides of the equation.

$- t = - 3$

Step 2.2

Divide each term in $- t = - 3$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- t = - 3$ by $- 1$ .

$\frac{- t}{- 1} = \frac{- 3}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{t}{1} = \frac{- 3}{- 1}$

Step 2.2.2.2

Divide $t$ by $1$ .

$t = \frac{- 3}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 3$ by $- 1$ .

$t = 3$

Step 3

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

Interval Notation:

$(- \infty, 3) \cup (3, \infty)$

Set-Builder Notation:

${t | t \neq 3}$

Step 4