Function's domain.Find the domain of definition of the function y = ln(x^2-3x+2) .

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The domain of logarithmic function is the interval ` (0,oo)` , hence, you need to set the following condition, such that:

`x^2-3x+2 in (0,oo) => x^2-3x+2 > 0`

You need to attach the quadratic equation, such that:

`x^2-3x+2 = 0`

`x^2 - (2 + 1)x + 2 = 0 => x^2 - 2x - x + 2 = 0`

You need to group the terms such that:

`(x^2 - 2x) - (x - 2) = 0 => x(x - 2) - (x - 2) = 0 => (x - 2)(x - 1) = 0`

Considering a value for` x in (1,2)` yields:

`x = 1.5 => 2.25 - 3*1.5 + 2 = -2.25 + 2 < 0`

Considering values for `x in (-oo,1)U(2,oo)` yields:

`x = 0.5 => 0.5^2-3*0.5+2 > 0`

`x = 3 => 9 - 9 + 2 > 0`

Hence, evaluating the domain of the function yields:

`x in (0,oo) nn {(-oo,1)U(2,oo)} => x in (0,1)U(2,oo)`

 

Hence, evaluating the domain of the basic logarithmic function yields that the function holds for `x in (0,1) U (2,oo).`

 

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