Find the value of m for which the function f(x) = { 3x + m, x < 1; 2x^2, x >= 1 is continuous at x = 1.
Practice Questions
1 question
Q1
Find the value of m for which the function f(x) = { 3x + m, x < 1; 2x^2, x >= 1 is continuous at x = 1.
-1
0
1
2
Setting 3(1) + m = 2(1)^2 gives m = -1.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of m for which the function f(x) = { 3x + m, x < 1; 2x^2, x >= 1 is continuous at x = 1.
Solution: Setting 3(1) + m = 2(1)^2 gives m = -1.
Steps: 7
Step 1: Understand that we need to find the value of m so that the function f(x) is continuous at x = 1.
Step 2: Recall that for a function to be continuous at a point, the left-hand limit and the right-hand limit at that point must be equal to the function's value at that point.
Step 3: Identify the two parts of the function: for x < 1, f(x) = 3x + m, and for x >= 1, f(x) = 2x^2.
Step 4: Calculate the left-hand limit as x approaches 1 from the left (x < 1): f(1) = 3(1) + m = 3 + m.
Step 5: Calculate the right-hand limit as x approaches 1 from the right (x >= 1): f(1) = 2(1)^2 = 2.
Step 6: Set the left-hand limit equal to the right-hand limit: 3 + m = 2.
Step 7: Solve for m: m = 2 - 3, which gives m = -1.
