Explanation Given information: The function, R ( x ) = x 3 + 6 x 2 − 4 x − 24 x 2 + 5 x − 14 . Explanation: Consider, R ( x ) = x 3 + 6 x 2 − 4 x − 24 x 2 + 5 x − 14 By factoring the numerator, ⇒ R ( x ) = x 2 ( x + 6 ) − 4 ( x + 6 ) x 2 + 5 x − 14 ⇒ R ( x ) = ( x 2 − 4 ) ( x + 6 ) x 2 + 5 x − 14 ⇒ R ( x ) = ( x + 2 ) ( x − 2 ) ( x + 6 ) x 2 + 5 x − 14 Now factoring the denominator ⇒ R ( x ) = ( x + 2 ) ( x − 2 ) ( x + 6 ) x 2 + 7 x − 2 x − 14 ⇒ R ( x ) = ( x + 2 ) ( x − 2 ) ( x + 6 ) x ( x + 7 ) − 2 ( x + 7 ) ⇒ R ( x ) = ( x + 2 ) ( x − 2 ) ( x + 6 ) ( x − 2 ) ( x + 7 ) The given function is rational function. Rational function is undefined where denominator is zero. Hence R ( x ) is undefined for ( x − 2 ) ( x + 7 ) = 0 . That is R ( x ) is undefined at x = 2 and, x = − 7

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Chapter 14, Problem 13CT

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The values where rational function R(x)=x3+6x2−4x−24x2+5x−14 is undefined and then find an asymptote or a hole appears at such numbers.

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Chapter 14, Problem 12CT

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The values where rational function R ( x ) = x 3 + 6 x 2 − 4 x − 24 x 2 + 5 x − 14 is undefined and then find an asymptote or a hole appears at such numbers.

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The values where rational function R(x)=x3+6x2−4x−24x2+5x−14 is undefined and then find an asymptote or a hole appears at such numbers.

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