For which value of a is the function f(x) = { ax + 1, x < 0; 2x + a, x >= 0 } continuous at x = 0?
Practice Questions
1 question
Q1
For which value of a is the function f(x) = { ax + 1, x < 0; 2x + a, x >= 0 } continuous at x = 0?
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Setting the two pieces equal at x = 0 gives 1 = a, hence a = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: For which value of a is the function f(x) = { ax + 1, x < 0; 2x + a, x >= 0 } continuous at x = 0?
Solution: Setting the two pieces equal at x = 0 gives 1 = a, hence a = 1.
Steps: 6
Step 1: Identify the function f(x) which has two parts: ax + 1 for x < 0 and 2x + a for x >= 0.
Step 2: To find the value of a that makes the function continuous at x = 0, we need to ensure that both parts of the function give the same output when x = 0.
Step 3: Calculate the output of the first part (ax + 1) when x = 0. This gives us f(0) = a(0) + 1 = 1.
Step 4: Calculate the output of the second part (2x + a) when x = 0. This gives us f(0) = 2(0) + a = a.
Step 5: Set the two outputs equal to each other: 1 = a.
