Continuous Function

[fr33pl4gu3]

Q.

Determine the constants a and b so that the function is continuous on the entire real line.

2 if x <= -1
f(x) = ax+b if -1 < x < 3
-2 if x >= 3

Ans:

a = 1; b = -1

I wonder if the answer is right??

[tiny-tim]

a = 1; b = -1

I wonder if the answer is right??

Almost … check it again … :wink:

[fr33pl4gu3]

Which one is wrong, a or b, or both??

[NoMoreExams]

Suppose your answer IS correct, that would mean

2 if x <= -1
f(x) = x - 1 if -1 < x < 3
-2 if x >= 3

However when x = -1, you get 2 (from the criterion x <= -1) and -2 for the criterion -1 < x < 3. Also when x = 3, you get 2 for the criterion -1 < x < 3 and -2 for the criterion x >= -3. You don't want those jumps if your f is cont.

[nicksauce]

Exactly. You shouldn't have to "wonder" if your answer is correct, you can check it yourself. Is the left-side limit of f(x) equal to the right-side limit at x=-1? at x = 3?

[matticus]

you have 2 linear equations with 2 unknowns

-a + b = 2
3a + b = -2