Find the domain of each of the following functions.(i) f(x) = x/(x2+3x

1.	Find the domain of each of the following functions.(i) f(x) = x/(x2+3x+2)(ii) f(x) = [x] + x
Answer» (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

Find the domain of each of the following functions.(i) f(x) = x/(x2+3x+2)(ii) f(x) = [x] + x

Answer»

(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