(i) f(x) = 1/x
As we know that, f(x) is defined for all real values of x, except for the case when x = 0.
∴ Domain of f = R – {0}
(ii) f(x) = 1/(x - 7)
As we know that, f (x) is defined for all real values of x, except for the case when x – 7 = 0 or x = 7.
∴ Domain of f = R – {7}
(iii) f(x) = (3x - 2)/(x + 1)
As we know that, f(x) is defined for all real values of x, except for the case when x + 1 = 0 or x = –1.
∴ Domain of f = R – {–1}
(iv) f(x) = (2x + 1)/(x2 - 9)
As we know that, f (x) is defined for all real values of x, except for the case when x2 – 9 = 0.
x2 – 9 = 0
x2 – 32 = 0
(x + 3)(x – 3) = 0
x + 3 = 0 or x – 3 = 0
x = ± 3
∴ Domain of f = R – {–3, 3}
(v) f(x) = (x2 + 2x + 1)/(x2 - 8x + 12)
As we know that, f(x) is defined for all real values of x, except for the case 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}