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
(
0
,
1
)
{\left(0 , 1 \right)}
(
0
,
1
)
(
1
,
−
8
)
{\left(1 , -8 \right)}
(
1
,
−
8
)
(
1
,
0
)
{\left(1 , 0 \right)}
(
1
,
0
)
(
−
8
,
1
)
{\left(-8 , 1 \right)}
(
−
8
,
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
↦
−
9
x
+
1
for
x
∈
R
,
0
≤
x
<
1.
{f: x \mapsto - 9 x + 1} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, 0 \leq x < 1.}
f
:
x
↦
−
9
x
+
1
for
x
∈
R
,
0
≤
x
<
1.
f
−
1
:
x
↦
−
1
9
x
+
1
9
for
x
∈
R
,
−
8
<
x
≤
1.
{f^{-1}: x \mapsto - \frac{1}{9} x + \frac{1}{9}} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -8<x\leq 1 .}
f
−
1
:
x
↦
−
9
1
x
+
9
1
for
x
∈
R
,
−
8
<
x
≤
1.
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