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in Differential equations by (50.2k points)

Find the domain of the function f(x) = log10(1 – log10(x2 – 5x + 16)) 

1 Answer

+1 vote
by (54.5k points)
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Best answer

Here, the function f is defined for

(1 – log10(x2 – 5x + 16)) > 0

⇒ log10(x2 – 5x + 16) < 1

⇒ (x2 – 5x + 16) < 10

⇒ (x2 – 5x + 6) < 0

⇒ (x – 2)(x – 3) < 0

⇒ 2 < x < 3

Thus, Df = (2, 3)

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