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Given the function f(x) = { (3x + 6, if x ≤ 3), (10x + 3, if 3 = 6) }, determine whether f(x) is continuous at x = 3.

User Chefsmart
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Final answer:

To determine if f(x) is continuous at x = 3, check if the left-hand limit and right-hand limit are equal.

Step-by-step explanation:

To determine whether the function f(x) is continuous at x = 3, we need to check if the left-hand limit and the right-hand limit of the function at x = 3 exist and are equal.

For the left-hand limit, we substitute x = 3 into the first part of the function: 3(3) + 6 = 15.

For the right-hand limit, we substitute x = 3 into the second part of the function: 10(3) + 3 = 33.

Since the left-hand limit (15) is not equal to the right-hand limit (33), the function f(x) is not continuous at x = 3.

User Kaj
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