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
,
−
5
)
{\left(0 , -5 \right)}
(
0
,
−
5
)
(
−
5
,
0
)
{\left(-5 , 0 \right)}
(
−
5
,
0
)
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
−
5
for
x
∈
R
,
x
>
0.
{f: x \mapsto - 4 x - 5} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x > 0.}
f
:
x
↦
−
4
x
−
5
for
x
∈
R
,
x
>
0.
f
−
1
:
x
↦
−
1
4
x
−
5
4
for
x
∈
R
,
x
<
−
5.
{f^{-1}: x \mapsto - \frac{1}{4} x - \frac{5}{4}} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, x < -5.}
f
−
1
:
x
↦
−
4
1
x
−
4
5
for
x
∈
R
,
x
<
−
5.
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