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Mathematics
Problem
Which of the following functions is non-differentiable? (a)
f
(
x
)
=
(
e
x
−
1
)
∣
e
2
x
−
1
∣
f(x)=(e^x-1)\lvert e^{2x}-1\rvert
f
(
x
)
=
(
e
x
−
1
)
∣
e
2
x
−
1
∣
in
R
\mathbb{R}
R
(b)
f
(
x
)
=
x
−
1
x
2
+
1
f(x)=\frac{x-1}{x^2+1}
f
(
x
)
=
x
2
+
1
x
−
1
in
R
\mathbb{R}
R
(c)
f
(
x
)
=
{
∣
∣
x
−
3
∣
−
1
∣
,
x
<
3
x
3
[
x
]
−
2
,
x
≥
3
f(x)=\begin{cases}\lvert\lvert x-3\rvert-1\rvert, & x<3\\ \frac{x}{3}[x]-2, & x\geq 3\end{cases}
f
(
x
)
=
{
∣∣
x
−
3
∣
−
1
∣
,
3
x
[
x
]
−
2
,
x
<
3
x
≥
3
at
x
=
3
x=3
x
=
3
where
[
⋅
]
[\cdot]
[
⋅
]
represents the greatest integer function (d)
f
(
x
)
=
3
(
x
−
2
)
1
/
3
+
3
f(x)=3(x-2)^{1/3}+3
f
(
x
)
=
3
(
x
−
2
)
1/3
+
3
in
R
\mathbb{R}
R
.
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