Answer:
p = 5/7
Step-by-step explanation:
The given function is:
for -4 ≦ x < 1
for 1 ≦ x ≦ 5
Part a)
A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5
The point where, g(x) stops during the first interval is at x = 1, which will be:
The point where g(x) starts during the second interval is:
For the function to be continuous, these two points must be equal. Setting them equal, we get:
3 = 7p - 2
3 + 2 = 7p
p =
Thus the value of p for which g(x) will be continuous is .
Part b)
We have to find p by setting the two pieces equal to each other. So, we get the equation as:
Substituting the point identified in part (a) i.e. x=1, we get:
This value agrees with the answer found in previous part.