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
,
−
9
)
{\left(-2 , -9 \right)}
(
−
2
,
−
9
)
(
−
9
,
−
2
)
{\left(-9 , -2 \right)}
(
−
9
,
−
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
↦
3
x
−
3
for
x
∈
R
,
x
≥
−
2.
{f: x \mapsto 3 x - 3} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x \geq -2.}
f
:
x
↦
3
x
−
3
for
x
∈
R
,
x
≥
−
2.
f
−
1
:
x
↦
1
3
x
+
1
for
x
∈
R
,
x
≥
−
9.
{f^{-1}: x \mapsto \frac{1}{3} x + 1} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x \geq -9.}
f
−
1
:
x
↦
3
1
x
+
1
for
x
∈
R
,
x
≥
−
9.
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