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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The domain of a function f(x) is the set of values that x can take for which f(x) is defined.

To determine the domain of `f(x) = (1 - x)/(x^3+x^2-2x)` , find the values of x for which f(x) is not defined.

f(x) = `(1 - x)/(x^3+x^2-2x)`

=> f(x) = `(1 - x)/(x*(x^2 + x - 2))`

=> f(x) = `(1 - x)/(x*(x^2 + 2x - x - 2))`

=> f(x) = `(1 - x)/(x*(x(x + 2) - 1(x + 2)))`

=> f(x) = `(1 - x)/(x*(x - 1)(x + 2))`

The denominator `(x*(x - 1)(x + 2))` is equal to 0 for x = 0, x = 1 and x = -2. The function f(x) is not defined when the denominator is 0.

This gives the domain of the function as all real numbers other than {-2, 0, 1}. The domain of the function `f(x) = (1 - x)/(x^3+x^2-2x)` is `R - {-2, 0, 1}`

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