Answer:
A. -4
Step-by-step explanation:
Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.
For the left hand limit;
The function at the left hand occurs at x<-1
f-(x) = x+3
f-(-1) = -1+3
f-(-1) = 2
For the right hand limit, the function occurs at x>-1
f+(x) = 2x-c
f+(-1) = 2(-1)-c
f+(-1) = -2-c
For the function f(x) to be continuous on the entire real line at x = -1, then
f-(-1) = f+(-1)
On equating both sides:
2 = -2-c
Add 2 to both sides
2+2 = -2-c+2
4 =-c
Multiply both sides by minus.
-(-c) = -4
c = -4
Hence the value of c so that f(x) is continuous on the entire real line is -4
The value of 'c' is -4 and this can be determined by using the concept of continuous function and arithmetic operations.
Given :
f(x) is continuous on the entire real line when c f(x) = x + 3 for [tex]x \leq -1[/tex], 2x - c for x > -1.
Remember for a continuous function, the left-hand limit is equal to the right-hand limit. So, determine the left-hand and right-hand limit.
The left-hand limit is calculated as:
f(-1) = (-1) + 3
f(-1) = 2 --- (1)
The right-hand limit is calculated as:
f(-1) = 2(-1) - c
f(-1) = -2 - c --- (2)
Now, equate both the expression (1) and (2).
2 = -2 - c
c = -4
For more information, refer to the link given below:
https://brainly.com/question/1111011
