Given, f(x)=√x and g(x)=√1−x ∴ Domain of f(x)=D1 is x≥0 i.e. D1:x∈(0,∞) and domain of g(x)=D2 is 1−x≥0⇒x≤1 i.e. D2:x∈(−∞1] As, we know that, the domain of f+g1f−g,g−f will be D1∩D2 as well as the domain for
f
g
is D1∩D2 except all those value(s) of x, such that g(x)=0. Similarly, for
g
f
is D1∩D2 but f(x)≠0. Hence, common domain for (f+g),(f−g),(