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
(
1
,
4
)
{\left(1 , 4 \right)}
(
1
,
4
)
(
4
,
1
)
{\left(4 , 1 \right)}
(
4
,
1
)
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
↦
x
+
3
for
x
∈
R
,
x
≥
1.
{f: x \mapsto x + 3} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x \geq 1.}
f
:
x
↦
x
+
3
for
x
∈
R
,
x
≥
1.
f
−
1
:
x
↦
x
−
3
for
x
∈
R
,
x
≥
4.
{f^{-1}: x \mapsto x - 3} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x \geq 4.}
f
−
1
:
x
↦
x
−
3
for
x
∈
R
,
x
≥
4.
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