To determine the continuity of the function f(x) = x^3 - x, we need to check three conditions:

1. The function f(x) is defined for all x in the real numbers. This is true because you can cube any real number and subtract the number itself.

2. The limit of f(x) as x approaches a certain value c exists for all c in the real numbers. This is also true because the limit of a polynomial function exists at every point in its domain.

3. The limit of f(x) as x approaches c is equal to f(c) for all c in the real numbers. This is true because for any c in the real numbers, the limit as x approaches c of x^3 - x is c^3 - c, which is f(c).

Since all three conditions are met, the function f(x) = x^3 - x is continuous for all x in the real numbers.

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To determine the continuity of the function f(x) = x^3 - x, we need to check three conditions:

1. The function f(x) is defined for all x in the real numbers. This is true because you can cube any real number and subtract the number itself.

2. The limit of f(x) as x approaches a certain value c exists for all c in the real numbers. This is also true because the limit of a polynomial function exists at every point in its domain.

3. The limit of f(x) as x approaches c is equal to f(c) for all c in the real numbers. This is true because for any c in the real numbers, the limit as x approaches c of x^3 - x is c^3 - c, which is f(c).

Since all three conditions are met, the function f(x) = x^3 - x is continuous for all x in the real numbers.

Knowee AI · Accepted Answer

To determine the continuity of the function f(x) = x^3 - x, we need to check three conditions:

1. The function f(x) is defined for all x in the real numbers. This is true because you can cube any real number and subtract the number itself.

2. The limit of f(x) as x approaches a certain value c exists for all c in the real numbers. This is also true because the limit of a polynomial function exists at every point in its domain.

3. The limit of f(x) as x approaches c is equal to f(c) for all c in the real numbers. This is true because for any c in the real numbers, the limit as x approaches c of x^3 - x is c^3 - c, which is f(c).

Since all three conditions are met, the function f(x) = x^3 - x is continuous for all x in the real numbers.

Determine the continuity of the function 𝑓𝑥=𝑥3-𝑥

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