Correct Answer - D
Let `g(x)=(1)/(log_(10)(1-x)) and h(x)=sqrt(x+2)`.
Then, ` f(x)=g(x)+h(x) . `
`:.` Domain (f) = Domain (g) ` cap` Domain (h)
Now, `g(x)=(1)/(log_(10)(1-x))` is defined , if
`1- x gt 0 and 1-x ne 1` i.e., ` x lt 1 and x ne 0`
So, domain (g) `=(-oo,1)-{0}` .
Clearly , `h(x)=sqrt(x+2)` is defined , `x+2 ge 0 , i.e., ge -2`
So , domain (h)`=[-2,oo)`
`:. ` Domain (f)`=(-oo,1)-{0} cap[-2,oo)=[-2,0) cup (0,1)`
