Functions Question 479
Question: The function $ f(x)=\max
[(1-x),,(1+x),,2], $ $ x\in (-\infty ,,\infty ), $ is [IIT 1995]
Options:
A) Continuous at all points
B) Differentiable at all points
C) Differentiable at all points except at $ x=1 $ and $ x=-1 $
D) Continuous at all points except at $ x=1 $ and $ x=-1 $ where it is discontinuous
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\max { (1-x),(1+x),2 },\forall x\in (-,\infty ,,\infty ). $ $ f(x)={ \begin{array}{*{35}{r}} 1+x; & x>1 \\ 2; & -1\le x\le 1 \\ 1-x; & x
\ $ f(x) $ is differentiable at all the points, except at
$ x=1 $ and at $ x=-1 $ …..(ii)
BETA
