(i) f is a rational function of the form g(x)/h(x), where g (x) = x and h (x) = x2 + 3x + 2.
Now h (x) ≠ 0 ⇒ x2 + 3x + 2 ≠ 0 ⇒ (x + 1) (x + 2) ≠ 0 and hence domain of the given function is R – {– 1, – 2}.
(ii) f (x) = [x] + x,i.e., f (x) = h (x) + g(x)
where h (x) = [x] and g (x) = x
The domain of h = R and the domain of g = R. Therefore
Domain of f = R
