How do you find the domain and range of g(x) = -11/(4 + x)?

Jul 17, 2018

The domain is $x \in \left(- \infty , 4\right) \cup \left(4 , + \infty\right)$. The range is $y \in \left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

Explanation:

The function is

$f \left(x\right) = - \frac{11}{4 + x}$

The denominator must be $\ne 0$

Therefore,

$4 + x \ne 0$

$x \ne - 4$

The domain is $x \in \left(- \infty , 4\right) \cup \left(4 , + \infty\right)$

To find the domain, Let

$y = - \frac{11}{4 + x}$

$y \left(4 + x\right) = - 11$

$y x + 4 y = - 11$

$y x = - 11 - 4 y$

$x = \frac{- 11 - 4 y}{y}$

The denominator must be $\ne 0$

$y \ne 0$

The range is $y \in \left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

graph{-11/(4+x) [-33.13, 18.18, -13.24, 12.43]}