Functions Question 234
Question: Let $ f(x)= \begin{cases} & x^{2}+k,\ \ \ \ when\ \ x\ge 0 \\ & -x^{2}-k,\ \ \text{when }x<0 \\ \end{cases} . $ . If the function $ f(x) $ be continuous at $ x=0 $ , then k =
Options:
A) 0
B) 1
C) 2
D) ?2
Show Answer
Answer:
Correct Answer: A
Solution:
Here $ \underset{x\to 0+}{\mathop{\lim }},f(x)=k,,\underset{x\to 0-}{\mathop{\lim }},f(x)=-k $ and $ f(0)=k $ But $ f(x) $ is continuous at $ x=0, $ therefore k must be zero.
BETA
