Find the domain of the function f(x) = (2x^3 - 5)/((x^2 + x - 6)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The domain of a function y = f(x) is the set of values of x for which y is defined.

For the given function `f(x) = (2x^3 - 5)/(x^2 + x - 6)` , the value of f(x) is defined in all cases where the value of the denominator x^2 + x - 6 is not zero. When the denominator is zero, the value of f(x) is not defined.

Solving x^2 + x - 6 = 0

x^2 + 3x - 2x - 6 = 0

x(x + 3) - 2(x + 3) = 0

(x - 2)(x + 3) = 0

x = 2 and x = -3

The domain of the function `f(x) = (2x^3 - 5)/(x^2 + x - 6)` is R - {-3, 2}

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