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Problem
Problem
Consider
f
:
x
→
2
x
f : x \rightarrow 2x
f
:
x
→
2
x
and
g
:
x
→
4
x
−
3
g : x \rightarrow 4x - 3
g
:
x
→
4
x
−
3
. a. a Find
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
. b. b Given
(
f
∘
g
)
−
1
(
k
)
=
2
(f \circ g)^{-1}(k) = 2
(
f
∘
g
)
−
1
(
k
)
=
2
, find
k
k
k
. c. c Show that
(
f
−
1
∘
g
−
1
)
(
x
)
=
(
g
∘
f
)
−
1
(
x
)
(f^{-1} \circ g^{-1})(x) = (g \circ f)^{-1}(x)
(
f
−
1
∘
g
−
1
)
(
x
)
=
(
g
∘
f
)
−
1
(
x
)
.
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