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To find the limit of f(x), when x approaches to - 1, first find the left hand side limit and then right hand side limit.

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The limit exists only, if the two limits i.e, left hand side limit and right hand side limit  would be the same.

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Means, that,

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The limit would be the same.So, the limit of the function f(x) is exists, where x approaches - 1

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The fact that f(- 1) = 5 has the value of the limit as x approaches - 1.

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Therefore, .

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The function f is defined at x = 1, since

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The limit

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(i). f(1) = 1 + 6 = 7.

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(ii). .

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(iii). and ,

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Therefore, .

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So, the three conditions are satisfied and the function is continues at the point 4.

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