For which value of k is the function f(x) = { kx + 1, x < 2; 3, x >= 2 } c
Practice Questions
Q1
For which value of k is the function f(x) = { kx + 1, x < 2; 3, x >= 2 } continuous at x = 2?
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Questions & Step-by-Step Solutions
For which value of k is the function f(x) = { kx + 1, x < 2; 3, x >= 2 } continuous at x = 2?
Step 1: Understand that for a function to be continuous at a point, the value of the function from the left side must equal the value from the right side at that point.
Step 2: Identify the point we are checking for continuity, which is x = 2.
Step 3: Look at the function definition: f(x) = kx + 1 for x < 2 and f(x) = 3 for x >= 2.
Step 4: Calculate the left-hand limit as x approaches 2. This means we use the part of the function for x < 2: f(2) = k(2) + 1.
Step 5: Calculate the right-hand limit as x approaches 2. This means we use the part of the function for x >= 2: f(2) = 3.
Step 6: Set the left-hand limit equal to the right-hand limit: 2k + 1 = 3.
