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

1. The function is defined for all real numbers. In this case, the function f(x) = x^3 - x is a polynomial, and polynomials are defined for all real numbers.

2. The limit of the function as x approaches a certain value from the left (denoted as x-a-) is equal to the limit of the function as x approaches that value from the right (denoted as x-a+). For all real numbers a, the limit as x approaches a from the left and right for the function f(x) = x^3 - x is the same, because the function is a polynomial and polynomials are continuous everywhere.

3. The limit of the function as x approaches a certain value is equal to the value of the function at that point. For all real numbers a, the limit as x approaches a for the function f(x) = x^3 - x is equal to f(a), because the function is a polynomial and polynomials are continuous everywhere.

Therefore, the function f(x) = x^3 - x is continuous for all real numbers.

Question

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

1. The function is defined for all real numbers. In this case, the function f(x) = x^3 - x is a polynomial, and polynomials are defined for all real numbers.

2. The limit of the function as x approaches a certain value from the left (denoted as x->a-) is equal to the limit of the function as x approaches that value from the right (denoted as x->a+). For all real numbers a, the limit as x approaches a from the left and right for the function f(x) = x^3 - x is the same, because the function is a polynomial and polynomials are continuous everywhere.

3. The limit of the function as x approaches a certain value is equal to the value of the function at that point. For all real numbers a, the limit as x approaches a for the function f(x) = x^3 - x is equal to f(a), because the function is a polynomial and polynomials are continuous everywhere.

Therefore, the function f(x) = x^3 - x is continuous for all 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 is defined for all real numbers. In this case, the function f(x) = x^3 - x is a polynomial, and polynomials are defined for all real numbers.

2. The limit of the function as x approaches a certain value from the left (denoted as x->a-) is equal to the limit of the function as x approaches that value from the right (denoted as x->a+). For all real numbers a, the limit as x approaches a from the left and right for the function f(x) = x^3 - x is the same, because the function is a polynomial and polynomials are continuous everywhere.

3. The limit of the function as x approaches a certain value is equal to the value of the function at that point. For all real numbers a, the limit as x approaches a for the function f(x) = x^3 - x is equal to f(a), because the function is a polynomial and polynomials are continuous everywhere.

Therefore, the function f(x) = x^3 - x is continuous for all real numbers.

Determine the continuity of the function fx=x3-x

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