f
(
x
)
=
4
x
−
6
Replace
f
(
x
)
with
y
.
y
=
4
x
−
6
Interchange the variables.
x
=
4
y
−
6
Solve for
y
.
Rewrite the equation as
4
y
−
6
=
x
.
4
y
−
6
=
x
Add
6
to both sides of the equation.
4
y
=
x
+
6
Divide each term by
4
and simplify.
y
=
x
4
+
3
2
Solve for
y
and replace with
f
−
1
(
x
)
.
Replace the
y
with
f
−
1
(
x
)
to show the final answer.
f
−
1
(
x
)
=
x
4
+
3
2
Set up the composite result function.
g
(
f
(
x
)
)
Evaluate
g
(
f
(
x
)
)
by substituting in the value of
f
into
g
.
4
x
−
6
4
+
3
2
Simplify terms.
g
(
4
x
−
6
)
=
2
x
−
3
+
3
2
Simplify the numerator.
g
(
4
x
−
6
)
=
2
x
2
Cancel the common factor of
2
.
g
(
4
x
−
6
)
=
x
Since
g
(
f
(
x
)
)
=
x
,
f
−
1
(
x
)
=
x
4
+
3
2
is the inverse of
f
(
x
)
=
4
x
−
6
.
f
−
1
(
x
)
=
x
4
+
3
2