Define the function f by
2x + 2 for x < 0
f(x) = ax + b for 0 < x < 3
4x - 5 for 3 < x
If a and b are chosen so as to make f(x) continuous everywhere, then a =
a. -4/3
b. -1/3
c. 2/3
d. 5/3
or none of these
2006-09-03 10:37:39 · 3 answers · asked by Olivia 4 in Education & Reference ➔ Higher Education (University +)
f(x) has to be continuous at x=0:
=> 2x+2 = ax + b at x=0
=> b=2
f(x) has to be continuous at x=3:
ax + b = 4x - 5 at x=3
=> ax + 2 = 4x - 5 (b=2)
=> 3a + 2 = 12 - 5 (x=3)
=> 3a = 12 - 5 - 2 = 5
=> a = 5/3
The answer is d.
2006-09-03 11:01:18 · answer #1 · answered by mitch_online_nl 3 · 0⤊ 0⤋
d.
a = 5/3
b = 2
2006-09-03 17:41:01 · answer #2 · answered by James B 1 · 0⤊ 0⤋
1 idk
2this would be cheating
2006-09-03 17:40:30 · answer #3 · answered by Kelsi W 2 · 0⤊ 1⤋