Functions Question 519
Question: The function ‘f’ is defined by $ f(x)=2x-1, $ if $ x>2 $ , $ f(x)=k\ $ if $ x=2 $ and $ x^{2}-1, $ if $ x<2 $ is continuous, then the value of k is equal to
[Pb. CET 2002]
Options:
A) 2
B) 3
C) 4
D) ?3
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ f(x)=2x-1, $ if $ x>2, $ $ f(x)=k, $ If $ x=2 $ and $ x^{2}-1, $ if $ x<2 $ , function is continuous. \ $ \underset{x\to 2}{\mathop{\lim }},f(x)=f(2) $ Þ $ \underset{x\to 2}{\mathop{\lim }},(2x-1)=k\Rightarrow k=3 $ .
BETA
