Find the domain of \( g \).

\[ g(x) = \frac{x+5}{2x^2 - x - 3} \]

g ( x ) = 2 x 2 − x − 3 x + 5 ​ D g ​ : 2 x 2 − x − 3  = 0 2 x 2 + 2 x − 3 x − 3  = 0 2 x ( x + 1 ) − 3 ( x + 1 )  = 0 ( x + 1 ) ( 2 x − 3 )  = 0 ⟺ x + 1  = 0 ∧ 2 x − 3  = 0 x  = − 1 ∧ x  = 1.5 D g ​ : x ∈ R \ { − 1 ; 1.5 }

Answered by Anonymous | 2024-06-10

The domain of the function g ( x ) = 2 x 2 − x − 3 x + 5 ​ includes all real numbers except x = − 2 3 ​ and x = 1 . Therefore, the domain can be written as R ∖ { − 2 3 ​ , 1 } .
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Answered by Anonymous | 2024-10-01