Determine if the function (f(x) = frac{x^2 - 4}{x - 2}) is continuous over the interval ([-2, 4]).

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Accepted Answer

Step:1 ：Step 1: We first find the domain of the function. The function is defined for all real numbers except at (x = 2), where the denominator is zero and the function is undefined.Step:2 ：Step 2: We then rewrite the function (f(x)) as (f(x) = (x + 2)) for all (x neq 2) by factoring the numerator and cancelling out the ((x - 2)) terms. This function is defined and continuous for all real numbers.Step:3 ：Step 3: Observe that the interval ([-2, 4]) includes the point (x = 2) where the original function is not defined. Therefore, the function (f(x) = frac{x^2 - 4}{x - 2}) is not continuous over the interval ([-2, 4]).

Answer

Step: 1 ：Step 1: We first find the domain of the function. The function is defined for all real numbers except at (x = 2), where the denominator is zero and the function is undefined.Step: 2 ：Step 2: We then rewrite the function (f(x)) as (f(x) = (x + 2)) for all (x neq 2) by factoring the numerator and cancelling out the ((x - 2)) terms. This function is defined and continuous for all real numbers.Step: 3 ：Step 3: Observe that the interval ([-2, 4]) includes the point (x = 2) where the original function is not defined. Therefore, the function (f(x) = frac{x^2 - 4}{x - 2}) is not continuous over the interval ([-2, 4]).

Determine if the function $f (x) = \frac{x^{2} - 4}{x - 2}$ is continuous over the interval $[- 2, 4]$ .

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Determine if the function f(x)=x2−4x−2 is continuous over the interval [−2,4].

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Popular Problems

Determine if the function $f (x) = \frac{x^{2} - 4}{x - 2}$ is continuous over the interval $[- 2, 4]$ .