Find the domain of each of the following real valued functions of real variable: f (x) = (x2+2x+1)/(x2-8x+12)
Find the domain of each of the following real valued functions of real variable: f (x) = (x2+2x+1)/(x2-8x+12)

Answer:

f(x) is defined for all real values of x, except when x2 – 8x + 12 = 0.

x2 – 8x + 12 = 0

x2 – 2x – 6x + 12 = 0

x(x – 2) – 6(x – 2) = 0

(x – 2)(x – 6) = 0

x – 2 = 0 or x – 6 = 0

x = 2 or 6

∴ Domain of f = R – {2, 6}