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
(
−
3
,
5
)
{\left(-3 , 5 \right)}
(
−
3
,
5
)
(
−
2
,
1
)
{\left(-2 , 1 \right)}
(
−
2
,
1
)
(
5
,
−
3
)
{\left(5 , -3 \right)}
(
5
,
−
3
)
(
1
,
−
2
)
{\left(1 , -2 \right)}
(
1
,
−
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
−
7
for
x
∈
R
,
−
3
<
x
≤
−
2.
{f: x \mapsto - 4 x - 7} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -3 < x \leq -2.}
f
:
x
↦
−
4
x
−
7
for
x
∈
R
,
−
3
<
x
≤
−
2.
f
−
1
:
x
↦
−
1
4
x
−
7
4
for
x
∈
R
,
1
≤
x
<
5.
{f^{-1}: x \mapsto - \frac{1}{4} x - \frac{7}{4}} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, 1\leq x<5 .}
f
−
1
:
x
↦
−
4
1
x
−
4
7
for
x
∈
R
,
1
≤
x
<
5.
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