Functions Question 38
If $ f(x)= \begin{cases} & ax^{2}-b,\text{when }0\le x\lt 1 \\ & 2,\text{when }x=1 \\ & x+1,\text{when }1 \lt x\le 2 \\ \end{cases} $
if continuous at $ x=1 $ , then the most suitable values of a, b are
[BIT Ranchi 1983]
Options:
A) $ a=2,\ b=0 $
B) $ a=1,\ b=-1 $
C) $ a=4,\ b=2 $
D) All of the above
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 1-}{\mathop{\lim }},f(x)=a-b,\underset{x\to 1+}{\mathop{\lim }},f(x)=2\Rightarrow a-b=2 $ All the given sets of a, b make $ f(x) $ continuous at x=1.
BETA
