Given the function f ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20 Describe where the function has a hole and how you found your answer.

Question

02-12-2019
Mathematics

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Given the function f ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20 Describe where the function has a hole and how you found your answer.

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Lidpras Lidpras · Answer 1 · 2019-12-02T14:49:22+01:00

Lidpras Lidpras

02-12-2019

[tex] {x}^{2} + 7x + \frac{10}{ {x}^{2} } + 9x + 20 \\ = {x}^{2} + 16x + \frac{10}{ {x}^{2} } + 20 \\ x = 0 \\ \frac{10}{ {x}^{2} } = \frac{10}{0} [/tex]

= undefined

It is undefined as you cannot divide by zero. Hence, there is a hole at x = 0.

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