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

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

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

domain

f (x) = \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

2 x - 3 y = 9, (2, 2)

y = x + 7 + x - 7

f (x) = 2 x^{3} + 6 x^{2} - 90 x + 5

lo g_{4} (x + 4) - 4

f (x) = \frac{4}{( x - 2 ) ^{2}}

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