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Mathematics
Mathematics
Problem
4. Show that the Modulus Function
f
:
R
→
R
f: \mathbf{R} \rightarrow \mathbf{R}
f
:
R
→
R
, given by
f
(
x
)
=
∣
x
∣
f(x)=|x|
f
(
x
)
=
∣
x
∣
, is neither oneone nor onto, where
∣
x
∣
|x|
∣
x
∣
is
x
x
x
, if
x
x
x
is positive or 0 and
∣
x
∣
|x|
∣
x
∣
is
−
x
-x
−
x
, if
x
x
x
is negative.
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