1.

Find the domain of (i) f(x) = ln (x – 5)(ii) f(x) = log10 (x – 5x + 6)

Answer»

(i) f(x) = ln (x – 5)

f is defined, when x – 5 > 0

∴ x > 5

∴ Domain of f = (5, ∞)

(ii) f(x) = log10 (x2 – 5x + 6)

x2 – 5x + 6 = (x – 2) (x – 3)

f is defined, when (x – 2) (x – 3) > 0

∴ x < 2 or x > 3

Solution of (x – a) (x – b) > 0 is x < a or x > b

where a < b

∴ Domain of f = (-∞, 2) ∪ (3, ∞)



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