What is the domain of ln|x-3|*sqrt((x-1)(5-x)) ?

The domain of ln|x-3|*sqrt((x-1)(5-x)) is 1<= x<3\lor 3<x<= 5

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domain of ln|x-3|*sqrt((x-1)(5-x))

domain

ln ∣ x - 3 ∣ \cdot (x - 1) (5 - x)

1 \leq x < 3 or 3 < x \leq 5

Interval Notation

[1, 3) \cup (3, 5]

Solution steps

Find non-negative values for radicals:

1 \leq x \leq 5

Find positive values for logs:

x < 3 or x > 3

Combine real regions and undefined points for final function domain

1 \leq x < 3 or 3 < x \leq 5

f (x) = 2 x^{2} - 8

f (x) = 2 e^{x - 2} + 3

f (x) = 2 x^{2} - 12 x + 13

f (x) = ln (x - 4) + x

f (x) = lo g_{7} (x + 2)

What is the domain of ln|x-3|*sqrt((x-1)(5-x)) ?
The domain of ln|x-3|*sqrt((x-1)(5-x)) is 1<= x<3\lor 3<x<= 5