Math Interactive
2. Functions
2.2. Inverse functions
2.2.4. Relationship
Important
The graphs of
f
f
f
and
f
−
1
f^{-1}
f
−
1
are symmetrical about the line
y
=
x
.
y=x.
y
=
x
.
Examples
x
{x}
x
y
{y}
y
(
−
2
,
−
6
)
{\left(-2 , -6 \right)}
(
−
2
,
−
6
)
(
−
6
,
−
2
)
{\left(-6 , -2 \right)}
(
−
6
,
−
2
)
y
=
f
(
x
)
{y=f(x)}
y
=
f
(
x
)
y
=
f
−
1
(
x
)
{y=f^{-1}(x)}
y
=
f
−
1
(
x
)
y
=
x
{y=x}
y
=
x
Get new example
f
:
x
↦
4
x
+
2
for
x
∈
R
,
x
<
−
2.
{f: x \mapsto 4 x + 2} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x < -2.}
f
:
x
↦
4
x
+
2
for
x
∈
R
,
x
<
−
2.
f
−
1
:
x
↦
1
4
x
−
1
2
for
x
∈
R
,
x
<
−
6.
{f^{-1}: x \mapsto \frac{1}{4} x - \frac{1}{2}} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x < -6.}
f
−
1
:
x
↦
4
1
x
−
2
1
for
x
∈
R
,
x
<
−
6.
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