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JEE Advanced 2014 Paper 1 Mathematics Q14
Mathematics
Problem
Let
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
and
g
:
R
→
R
g:\mathbb R\to\mathbb R
g
:
R
→
R
be respectively given by
f
(
x
)
=
∣
x
∣
+
1
f(x)=|x|+1
f
(
x
)
=
∣
x
∣
+
1
and
g
(
x
)
=
x
2
+
1
g(x)=x^2+1
g
(
x
)
=
x
2
+
1
. Define
h
:
R
→
R
h:\mathbb R\to\mathbb R
h
:
R
→
R
by
h
(
x
)
=
{
max
{
f
(
x
)
,
g
(
x
)
}
,
x
≤
0
,
min
{
f
(
x
)
,
g
(
x
)
}
,
x
>
0.
h(x)=\begin{cases}\max\{f(x),g(x)\},&x\leq0,\\\min\{f(x),g(x)\},&x>0.\end{cases}
h
(
x
)
=
{
max
{
f
(
x
)
,
g
(
x
)}
,
min
{
f
(
x
)
,
g
(
x
)}
,
x
≤
0
,
x
>
0.
The number of points at which
h
(
x
)
h(x)
h
(
x
)
is not differentiable is
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