The domain of the function g (x) = (x² - 2 x - 15) / (x² + x - 6) is R - {-3, 2}.
We are given a function:
g (x) = (x² - 2 x - 15) / (x² + x - 6)
We need to find the domain of the function.
We know that a function becomes not defined when the denominator becomes 0.
Put x² + x - 6 = 0
x² + 3 x - 2 x - 6 = 0
x (x + 3) - 2( x + 3) = 0
( x + 3 ) ( x - 2 ) = 0
We get x = - 3 and x = 2.
So, these cannot be the values of x
So, the domain is
Domain = R - {-3, 2}
Therefore, the domain of the function g (x) = (x² - 2 x - 15) / (x² + x - 6) is R - {-3, 2}.
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