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Problem
Problem
For each of the following functions
f
f
f
: - Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
. - Sketch
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
,
y
=
f
−
1
(
x
)
y = f^{-1}(x)
y
=
f
−
1
(
x
)
, and
y
=
x
y = x
y
=
x
on the same set of axes. - Show that
(
f
−
1
∘
f
)
(
x
)
=
(
f
∘
f
−
1
)
(
x
)
=
x
(f^{-1} \circ f)(x) = (f \circ f^{-1})(x) = x
(
f
−
1
∘
f
)
(
x
)
=
(
f
∘
f
−
1
)
(
x
)
=
x
, the identity function. a. a
f
:
x
→
2
x
+
5
f : x \rightarrow 2x + 5
f
:
x
→
2
x
+
5
b. b
f
:
x
→
3
−
2
x
4
f : x \rightarrow \frac{3-2x}{4}
f
:
x
→
4
3
−
2
x
c. c
f
:
x
→
x
+
3
f : x \rightarrow x + 3
f
:
x
→
x
+
3
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