Answers: (i) Now we have, f(x) is defined for all real numbers x. Domain (f) = R If x < 0, –|x| < 0 f (x) < 0 If x ≥ 0, –x ≤ 0. –|x| ≤ 0 ⇒ f (x) ≤ 0 ∴ f (x) ≤ 0 or f (x) ∈ (–∞, 0] Range (f)...

Answers: (i) f(x) is defined for all real values of x, except when 2 – x = 0 or x = 2. Domain (f) = R – {2} f (x) = (x-2)/(2-x) f (x) = -(2-x)/(2-x) = –1 If x ≠ 2, f(x) = –1 ∴ Range (f) = {–1} (ii)...

Answers: (i) Square of a real number is not negative. f(x) takes real values only when x – 1 ≥ 0 x ≥ 1 ∴ x ∈ [1, ∞) Domain (f) = [1, ∞) If x ≥ 1 x – 1 ≥ 0 √(x-1) ≥ 0 ⇒ f (x) ≥ 0 f(x) ∈ [0, ∞) ∴...

Answers: (i) f(x) is defined for all real values of x, except when bx – a = 0 or x = a/b. Domain (f) = R – (a/b) Consider, f (x) = y (ax+b)/(bx-a) = y ax + b = y(bx – a) ax + b = bxy – ay ax – bxy...

Answers: (i) Square of a real number is not negative. f (x) takes real values only when 9 – x2 ≥ 0 9 ≥ x2 x2 ≤ 9 x2 – 9 ≤ 0 x2 – 32 ≤ 0 (x + 3)(x – 3) ≤ 0 x ≥ –3 and x ≤ 3 x ∈ [–3, 3] ∴ Domain (f) =...

Answers: (i) Square of a real number is not negative. f (x) takes real values only when x – 2 ≥ 0 x ≥ 2 ∴ x ∈ [2, ∞) ∴ Domain (f) = [2, ∞) (ii) Square of a real number is not negative. f (x) takes...

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 ∴...

Answers: (i) f(x) is defined for all real values of x, except when x + 1 = 0 or x = –1. ∴ Domain of f = R – {–1} (ii) f (x) is defined for all real values of x, except when x2 – 9 = 0. x2 – 9 = 0...

Answers: (i) f (x) is defined for all real values of x, except when x = 0. ∴ Domain of f = R – {0} (ii) f (x) is defined for all real values of x, except when x – 7 = 0 or x = 7. ∴ Domain of f = R –...

Answer: f {f (x)} = f {1/(1 – x)} f {f (x)} = 1 / 1 – (1/(1 – x)) f {f (x)} = 1 / [(1 – x – 1)/(1 – x)] f {f (x)} = 1 / (-x/(1 – x)) f {f (x)} = (1 – x) / -x f {f (x)} = (x – 1) / x ∴ f {f (x)} = (x...

Solutions: (v) g/f We know, (g/f) (x) = g(x)/f(x) (g/f) (x) = √(9-x2) / √(x+1) = √[(9-x2) / (x+1)] Domain of g/f = Domain of f ∩ Domain of g = [–1, ∞) ∩ [–3, 3] = [–1, 3] However, (g/f) (x) is...