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What are the domain and the range of function ? f(x)=x-6/x^2-3x-18​

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Answer:The domain of the function is x ∈ R − { − 3 } . The range is y ∈ R − { 1 } Explanation: Factorise the numerator and denominator y = x 2 − 5 x − 6 x 2 − 3 x − 18 = ( x + 1 ) x − 6 ( x + 3 ) x − 6 = x + 1 x + 3 The denominator is ≠ 0 , therefore x + 3 ≠ 0 , ⇒ , x ≠ − 3 The domain of the function is x in RR-{-3} To determine the range, proceed as follows y = x + 1 x + 3 y ( x + 3 ) = x + 1 y x − x = 1 − 3 y x ( y − 1 ) = 1 − 3 y x = 1 − 3 y y − 1 The denominator is ≠ 0 y − 1 ≠ 0 , ⇒ , y ≠ 1 The range is y ∈ R − { 1 } graph{(x^2-5x-6)/(x^2-3x-18) [-16.02, 16.02, -8.01, 8.01]}

Step-by-step Explanation: Factorise the numerator and denominator y = x 2 − 5 x − 6 x 2 − 3 x − 18 = ( x + 1 ) x − 6 ( x + 3 ) x − 6 = x + 1 x + 3 The denominator is ≠ 0 , therefore x + 3 ≠ 0 , ⇒ , x ≠ − 3 The domain of the function is x in RR-{-3} To determine the range, proceed as follows y = x + 1 x + 3 y ( x + 3 ) = x + 1 y x − x = 1 − 3 y x ( y − 1 ) = 1 − 3 y x = 1 − 3 y y − 1

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