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Mathematics
Mathematics
Problem
Define
f
:
[
0
,
∞
)
→
[
2
,
∞
)
f:[0,\infty)\to[2,\infty)
f
:
[
0
,
∞
)
→
[
2
,
∞
)
by
f
(
x
)
=
x
2
+
2
f(x)=x^{2}+2
f
(
x
)
=
x
2
+
2
. a. (a) Prove that
f
f
f
is bijective. b. (b) Find
f
−
1
f^{-1}
f
−
1
and state its domain and co-domain. c. (c) Show that
f
−
1
(
f
(
x
)
)
=
x
f^{-1}\bigl(f(x)\bigr)=x
f
−
1
(
f
(
x
)
)
=
x
for all
x
∈
[
0
,
∞
)
x\in[0,\infty)
x
∈
[
0
,
∞
)
and that
f
(
f
−
1
(
y
)
)
=
y
f\bigl(f^{-1}(y)\bigr)=y
f
(
f
−
1
(
y
)
)
=
y
for all
y
∈
[
2
,
∞
)
y\in[2,\infty)
y
∈
[
2
,
∞
)
.
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