Where is the function f(x) = ln((x - 1)/(x +2)) not continuous.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function `f(x) = ln((x - 1)/(x +2))` . If a function is continuous at x = a, it has to be defined at x = a.

The logarithmic function is defined only for values greater than 0.

It is not defined in the following case: `(x - 1)/(x +2) <= 0`

=> x - 1 `<=` 0 and x + 2 `>=` 0 or x - 1 `>=` 0 and x + 2 `<=` 0

=> x `<= ` 1 and x `>=` -2 or x `>=` 1 and x `<=` -2

x cannot be greater than 1 and less than -2 at the same time.

The condition `(x - 1)/(x +2) <= 0` is true in [-2, 1]

The function f(x) is not continuous in [-2, 1]

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