Find the Domain f(x)=(3x)/(7-x)

$f (x) = \frac{3 x}{7 - x}$

Step 1

Set the denominator in $\frac{3 x}{7 - x}$ equal to $0$ to find where the expression is undefined.

$7 - x = 0$

Step 2

Solve for $x$ .

Subtract $7$ from both sides of the equation.

$- x = - 7$

Divide each term in $- x = - 7$ by $- 1$ and simplify.

Divide each term in $- x = - 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 7}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$x = 7$

Step 3

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

Interval Notation:

$(- \infty, 7) \cup (7, \infty)$

Set-Builder Notation:

${x | x \neq 7}$

Step 4