Question
If $$f$$ and $$g$$ are two functions defined as $$f\left( x \right) = x + 2,\,x \leqslant 0;\,g\left( x \right) = 3,\,x \geqslant 0,$$ then the domain of $$f + g$$ is :
A.
$$\left\{ 0 \right\}$$
B.
$$\left[ {0,\,\infty } \right)$$
C.
$$\left( { - \infty ,\,\infty } \right)$$
D.
$$\left( { - \infty ,\,0} \right)$$
Answer :
$$\left\{ 0 \right\}$$
Solution :
$$\eqalign{
& D\left( {f + g} \right) = D\left( f \right) \cap D\left( g \right) \cr
& = \left( { - \infty ,\,0} \right] \cap \left[ {0,\,\infty } \right) \cr
& = \left\{ 0 \right\} \cr} $$