Functions Part 1

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+g,f−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),(‌

f

g

),(‌

g

f

) and (g−f)
will be 0<x<1.