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
,
−
5
)
{\left(-1 , -5 \right)}
(
−
1
,
−
5
)
(
1
,
7
)
{\left(1 , 7 \right)}
(
1
,
7
)
(
−
5
,
−
1
)
{\left(-5 , -1 \right)}
(
−
5
,
−
1
)
(
7
,
1
)
{\left(7 , 1 \right)}
(
7
,
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
↦
6
x
+
1
for
x
∈
R
,
−
1
≤
x
≤
1.
{f: x \mapsto 6 x + 1} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -1 \leq x \leq 1.}
f
:
x
↦
6
x
+
1
for
x
∈
R
,
−
1
≤
x
≤
1.
f
−
1
:
x
↦
1
6
x
−
1
6
for
x
∈
R
,
−
5
≤
x
≤
7.
{f^{-1}: x \mapsto \frac{1}{6} x - \frac{1}{6}} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -5\leq x\leq 7 .}
f
−
1
:
x
↦
6
1
x
−
6
1
for
x
∈
R
,
−
5
≤
x
≤
7.
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