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Mathematics
Mathematics
Problem
Which of the following functions, with the indicated domain, is NOT one–one? a)
f
2
:
R
→
R
,
f
2
(
x
)
=
e
x
f_2:\mathbb{R}\to\mathbb{R},\;f_2(x)=e^{x}
f
2
:
R
→
R
,
f
2
(
x
)
=
e
x
b)
f
4
:
R
→
R
,
f
4
(
x
)
=
x
2
+
1
f_4:\mathbb{R}\to\mathbb{R},\;f_4(x)=x^{2}+1
f
4
:
R
→
R
,
f
4
(
x
)
=
x
2
+
1
c)
g
:
[
0
,
∞
)
→
R
,
g
(
x
)
=
x
2
+
1
g:[0,\infty)\to\mathbb{R},\;g(x)=x^{2}+1
g
:
[
0
,
∞
)
→
R
,
g
(
x
)
=
x
2
+
1
d)
f
3
:
(
0
,
∞
)
→
R
,
f
3
(
x
)
=
ln
x
f_3:(0,\infty)\to\mathbb{R},\;f_3(x)=\ln x
f
3
:
(
0
,
∞
)
→
R
,
f
3
(
x
)
=
ln
x
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