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
(
−
4
,
−
5
)
{\left(-4 , -5 \right)}
(
−
4
,
−
5
)
(
0
,
7
)
{\left(0 , 7 \right)}
(
0
,
7
)
(
−
5
,
−
4
)
{\left(-5 , -4 \right)}
(
−
5
,
−
4
)
(
7
,
0
)
{\left(7 , 0 \right)}
(
7
,
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
↦
3
x
+
7
for
x
∈
R
,
−
4
≤
x
≤
0.
{f: x \mapsto 3 x + 7} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -4 \leq x \leq 0.}
f
:
x
↦
3
x
+
7
for
x
∈
R
,
−
4
≤
x
≤
0.
f
−
1
:
x
↦
1
3
x
−
7
3
for
x
∈
R
,
−
5
≤
x
≤
7.
{f^{-1}: x \mapsto \frac{1}{3} x - \frac{7}{3}} \allowbreak \quad \allowbreak {\textrm{for } x \in \mathbb{R}, -5\leq x\leq 7 .}
f
−
1
:
x
↦
3
1
x
−
3
7
for
x
∈
R
,
−
5
≤
x
≤
7.
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