What is the domain of 1/(ln(-x^2+4x-3)) ?

The domain of 1/(ln(-x^2+4x-3)) is 1<x<2\lor 2<x<3

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domain of 1/(ln(-x^2+4x-3))

domain

\frac{1}{ln ( - x ^{2} + 4 x - 3 )}

1 < x < 2 or 2 < x < 3

Interval Notation

(1, 2) \cup (2, 3)

Solution steps

Find positive values for logs:

1 < x < 3

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

1 < x < 2 or 2 < x < 3

f (x) = \frac{3 x}{1 + 9 x ^{2}}

\frac{x ^{2} + 3 x}{x + 3}

ln (4 - x^{2})

(7 - 4) \frac{2}{3}

- x^{4} + 2 x^{3}

What is the domain of 1/(ln(-x^2+4x-3)) ?
The domain of 1/(ln(-x^2+4x-3)) is 1<x<2\lor 2<x<3