Find the Domain g(t)=(4-5t)/(1-2t)

$g (t) = \frac{4 - 5 t}{1 - 2 t}$

Step 1

Set the denominator in $\frac{4 - 5 t}{1 - 2 t}$ equal to $0$ to find where the expression is undefined.

$1 - 2 t = 0$

Step 2

Solve for $t$ .

Subtract $1$ from both sides of the equation.

$- 2 t = - 1$

Divide each term in $- 2 t = - 1$ by $- 2$ and simplify.

Divide each term in $- 2 t = - 1$ by $- 2$ .

$\frac{- 2 t}{- 2} = \frac{- 1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 t}{- 2} = \frac{- 1}{- 2}$

Divide $t$ by $1$ .

$t = \frac{- 1}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$t = \frac{1}{2}$

Step 3

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

Interval Notation:

$(- \infty, \frac{1}{2}) \cup (\frac{1}{2}, \infty)$

Set-Builder Notation:

${t | t \neq \frac{1}{2}}$

Step 4