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Determine the value of c for which the function f(x) = { 3x + c, x < 1; 2x^2
Determine the value of c for which the function f(x) = { 3x + c, x < 1; 2x^2 - 1, x >= 1 } is continuous at x = 1.
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Practice Questions
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Q1
Determine the value of c for which the function f(x) = { 3x + c, x < 1; 2x^2 - 1, x >= 1 } is continuous at x = 1.
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Setting the two pieces equal at x = 1 gives us 3 + c = 1. Thus, c = -2.
Questions & Step-by-step Solutions
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Q
Q: Determine the value of c for which the function f(x) = { 3x + c, x < 1; 2x^2 - 1, x >= 1 } is continuous at x = 1.
Solution:
Setting the two pieces equal at x = 1 gives us 3 + c = 1. Thus, c = -2.
Steps: 6
Show Steps
Step 1: Identify the two pieces of the function f(x). The first piece is 3x + c for x < 1, and the second piece is 2x^2 - 1 for x >= 1.
Step 2: Find the value of the first piece when x is equal to 1. Substitute x = 1 into the first piece: 3(1) + c = 3 + c.
Step 3: Find the value of the second piece when x is equal to 1. Substitute x = 1 into the second piece: 2(1)^2 - 1 = 2 - 1 = 1.
Step 4: Set the two results from Step 2 and Step 3 equal to each other to ensure continuity at x = 1: 3 + c = 1.
Step 5: Solve for c by isolating it: c = 1 - 3.
Step 6: Calculate the value of c: c = -2.
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