(a) let f : R → R be a function defined by
f(x) = x + 4 if x ≤ 1
ax + b if 1 < x ≤ 3
3x − 8 if x > 3
Find the values of a and b that makes f(x) continuous on R.
1
Expert's answer
2020-06-29T18:21:46-0400
The function should be continuous, so "\\lim_{x\\to 1+} (ax+b) = f(1) \\;\\; \\mathrm{and} \\;\\; \\lim_{x\\to 3+} (3x-8) = f(3)." Therefore, "a+b = 1+4, \\;\\; 9-8 = 3a+b."
"a+b=5, \\;\\; 1=3a+b." Solving this system, we get , "a = -2" and "b=7."
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