Find the Domain and Range f^-1(x)=(2x+1)/(5+x)

$f^{- 1} (x) = \frac{2 x + 1}{5 + x}$

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

$5 + x = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

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

Interval Notation:

$(- \infty, - 5) \cup (- 5, \infty)$

Set-Builder Notation:

${x | x \neq - 5}$

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, 2) \cup (2, \infty)$

Set-Builder Notation:

${y | y \neq 2}$

Determine the domain and range.

Domain: $(- \infty, - 5) \cup (- 5, \infty), {x | x \neq - 5}$

Range: $(- \infty, 2) \cup (2, \infty), {y | y \neq 2}$