Functions Question 282
The function $ f(x),= \begin{cases} & x+2,,1\le x\le 2 \\ & 4,,,x=2 \\ & 3x-2,,x>2 \\ \end{cases} . $ is continuous at x = 2
[DCE 1999]
Options:
A) $ x=2 $ only
B) $ x\le 2 $
C) $ x\ge 2 $
D) None of these
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Answer:
Correct Answer: C
Solution:
Clearly the function is defined only in the interval $ [1,,\infty ) $ hence option cannot even apply. For $ x>2,,y=3x-2 $ which is a straight line, hence continuous. Further $ y=4 $ at $ x=2 $ . Hence, the function is continuous at $ x=2 $ also (but not only at $ x=2 $ ).
BETA
