For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1

For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?

For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?

Step 1: Identify the function f(x) which has two parts: f(x) = 3x + c for x < 1 and f(x) = 2x^2 for x >= 1.
Step 2: To find the value of c that makes the function continuous at x = 1, we need to ensure that the two parts of the function meet at that point.
Step 3: Calculate the value of f(x) when x = 1 using the first part of the function: f(1) = 3(1) + c.
Step 4: Calculate the value of f(x) when x = 1 using the second part of the function: f(1) = 2(1)^2.
Step 5: Set the two results equal to each other: 3(1) + c = 2(1)^2.
Step 6: Simplify the equation: 3 + c = 2.
Step 7: Solve for c by subtracting 3 from both sides: c = 2 - 3.
Step 8: Find the value of c: c = -1.

Continuity of Piecewise Functions – The question tests the understanding of how to ensure continuity at a point for piecewise functions by equating the limits from both sides.