# How do you find the domain of f+g given f(x) = (7x)/(x+6) and g(x)= 4/(x+1)?

Dec 31, 2017

${D}_{f + g} = {D}_{f} \cap {D}_{g} = \mathbb{R} - \left\{- 1 , - 6\right) =$
$\left(- \infty , - 6\right) \cup \left(- 6 , - 1\right) \cup \left(- 1 , + \infty\right)$

#### Explanation:

$f \left(x\right) = \frac{7 x}{x + 6}$

D_f={AA$x$$\in \mathbb{R}$:x+6!=0} $= \mathbb{R} - \left\{- 6\right\} = \left(- \infty , - 6\right) \cup \left(- 6 , + \infty\right)$

$g \left(x\right) = \frac{4}{x + 1}$

D_g={AA$x$$\in \mathbb{R}$:x+1!=0} $= \mathbb{R} - \left\{- 1\right\} = \left(- \infty , - 1\right) \cup \left(- 1 , + \infty\right)$

${D}_{f + g} = {D}_{f} \cap {D}_{g} = \mathbb{R} - \left\{- 1 , - 6\right) =$
$\left(- \infty , - 6\right) \cup \left(- 6 , - 1\right) \cup \left(- 1 , + \infty\right)$