Question
If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true?
I. g(x) = 1 at least once
II. lim g(x) = g(3.5) as x aproaches 3.5.
III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches from the right
A. I only
B. II only
C. I and II only
D. I, II, and III
E. None of these.
I want to say that the answer should be D. I, II, and III since the function is continuous for all real numbers. Would this be correct?
I. g(x) = 1 at least once
II. lim g(x) = g(3.5) as x aproaches 3.5.
III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches from the right
A. I only
B. II only
C. I and II only
D. I, II, and III
E. None of these.
I want to say that the answer should be D. I, II, and III since the function is continuous for all real numbers. Would this be correct?
Answers
Sagar
Yes that is correct because if it's continuous then it must pass through 1 and the limit must exist at 3.5 and the limit must equal the same from both sides. So the answer is D (I,II,II)