Question

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

Answer 1

`D_(f+g)=D_fnnD_g=RR-{-1,-6)=`
`(-oo,-6)uu(-6,-1)uu(-1,+oo)`

Explanation:

`f(x)=(7x)/(x+6)`

`D_f={AA` `x` `inRR` `:x+6!=0}` `=RR-{-6}=(-oo,-6)uu(-6,+oo)`

`g(x)=4/(x+1)`

`D_g={AA` `x` `inRR` `:x+1!=0}` `=RR-{-1}=(-oo,-1)uu(-1,+oo)`

`D_(f+g)=D_fnnD_g=RR-{-1,-6)=`
`(-oo,-6)uu(-6,-1)uu(-1,+oo)`