Given f (x) =

x2+2x+1

x2−8x+12

Here, f(x) is a rational function of x as

x2+2x+1

x2−8x+12

is a rational expression.
∴ f(x) assumes real values ∀ x except for the values of x for which
x2 – 8x + 12 = 0 i.e., (x – 6) (x – 2) = 0 ⇒ x = 6, 2
∴ Domain of f (x) = R – {2, 6}.