Question

Givin the folloring function: f(x)={(3x+6 if x<=3),(10x+3, if 3=6):} Dofirminp whither f(x) is continuous at: x=3

Answer 1

To determine if the function f(x) is continuous at x = 3, we need to check if the function's limit from both the left and right side of 3 is equal to the function's value at x = 3. Since the limit from the left side (15) is not equal to the limit from the right side (33), f(x) is not continuous at x = 3.

Step-by-step explanation:

To determine if the function f(x) is continuous at x = 3, we need to check if the function's limit from both the left and right side of 3 is equal to the function's value at x = 3.

From the left side, as x approaches 3, the value of f(x) is 3x + 6. Plugging in 3, we get f(3) = 3(3) + 6 = 15.

From the right side, as x approaches 3, the value of f(x) is 10x + 3. Plugging in 3, we get f(3) = 10(3) + 3 = 33.

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