The function f(x) = { x^2, x < 2; k, x = 2; 3x - 4, x > 2 } is continuous at x = 2 for which value of k?
Practice Questions
1 question
Q1
The function f(x) = { x^2, x < 2; k, x = 2; 3x - 4, x > 2 } is continuous at x = 2 for which value of k?
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To be continuous at x = 2, k must equal f(2) = 2^2 = 4.
Questions & Step-by-step Solutions
1 item
Q
Q: The function f(x) = { x^2, x < 2; k, x = 2; 3x - 4, x > 2 } is continuous at x = 2 for which value of k?
Solution: To be continuous at x = 2, k must equal f(2) = 2^2 = 4.
Steps: 5
Step 1: Understand that a function is continuous at a point if the limit of the function as it approaches that point from both sides is equal to the value of the function at that point.
Step 2: Identify the point we are interested in, which is x = 2.
Step 3: Calculate the value of the function f(x) when x is less than 2. This is given by f(x) = x^2. So, find f(2) using this part: f(2) = 2^2 = 4.
Step 4: Identify the value of the function at x = 2, which is given as k. So, f(2) = k.
Step 5: For the function to be continuous at x = 2, we need k to equal the value we found in Step 3. Therefore, set k = 4.
