Find the domain of each of the following real valued functions of real variable:

(i) f(x) = $$\dfrac{1}{x}$$

(ii) f(x) = $$\dfrac{1}{(x-7)}$$

(iii) f(x) = $$\dfrac{ (3x-2)}{(x+1)}$$

(iv) f(x) = $$\dfrac{ (2x+1)}{(x^2-9)}$$

(v) f(x) = $$\dfrac{ (x^2+2x+1)}{(x^2-8x+12)}$$

Asked by Sakshi | 1 year ago |  146

##### Solution :-

(i) We know, f (x) is defined for all real values of x, except for the case when x = 0.

Domain of f = R – {0}

(ii) We know, 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) We know, 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) We know, 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) We know, 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}

Answered by Sakshi | 1 year ago

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