```     Ó
3 −  + 2
①   =
+2
= ℝ − {−}
< −∞, − >∪< −, +∞ >
La Función no
tiene inversa
¿Tendrá inversa?
|  =
( + 2)(−1 + 2) −(3 −  +  2 )
( + 2)2
2 + 4 − 5
≤0
( + 2)2
2 + 4 − 5
≥0
( + 2)2
2 + 4 − 5 ≥ 0
( + 4)( − 1) ≥ 0
+ −4 − 1 +
< −∞, −4] ∪ [1, +∞ >
2 + 4 − 5
=
( + 2)2
+ ≠
≠ −
[−4,1]
[(−4), (1)]
23
[− , 1]
2
−  +
②   =
[−,  >
+
¿Tendrá inversa?
í, á
[ −1 ,  1 > = [5,1 >
¿ ?
Ó
②   = ( − 3)2 −5    = [−3,3]
= ( − 3)2 −5
+ 5 = ( − 3)2
¿Tendrá inversa en [1,6]?
′  = 2( − 3)
+5=−3
2( − 3) ≥ 0
−
3
+5+3=
+
[3, +∞ >
+ 5 + 3 = ()
⇒
( − ) ≤
< −∞, 3]
¿ á   ó ?
⇒
ó
:
1
′  =
2 +5
ó:   = −  ; ∗ () =  +  +
( ∗ )′  =
1
2 +5
= (
− 3)2 −5

( ∗ )′
¿ á   ó ?
= ( − 3)2 −5
+ 5 = ( − 3)2
+5=−3
−1 = ( − 3)2 −5
:
′ −1 =
0 = ( − 3)2 −5 + 1
1
0 = ( − 3)2 −4
2 +5
2 −1 + 5
′  = 2( − 3)
1
1

∗
=
=
( )′  =
( − ) 2(5 − 3) 4

1
( )′ −1 =
=−
(− − )
8
+ 5 + 3 = ()
1

′()
∗
+5+3=
′  =
−1
: (∗ )′  =
0 = ( − 3 + 2)( − 3 − 2)
=
1
4
0 = ( − 1)( − 5)
=1 =5
2( − 3) ≥ 0
[3, +∞ >

(∗ )′  =
= ()
= ()

1

=
=
′()
()
−
′  = ()
= ()
= ()
() = ()
∗ () = ()
= ()
∗ () = ()
1

1 − 2

1

=−
=−
′()
()
−
= ()
(∗ )′  =
1−
2
1

= ()
∗ () = ()
(∗ )′
1

=
=
=
2 ()
+
′()
= ()

1 + 2
1

1
=
⇒
= ()
=
⇒
= ()
() = −
=
⇒
= ()
()
Ct  =
⇒
= ()
=
⇒
=
⇒
= ()
= ()
() =
1−
2

1
2
1−

1
=

1 + 2
1
() = −

1 + 2
()
=
1
2

() = −
−1

1

2 − 1

∆
= Pendiente =
∆
+ ∆ − () ()
=
∆→0

∆
lim
∆ ()
=
∆

¿  ?
+ ∆ − () ()
=
∆

= 36 +
∆ = 1
1
2 36 +
Razón de cambio
Rapidez de cambio
Rapidez instantánea
+ ∆ −   = ∆ . ′()
−   = ∆ . ′()
= 0, ⇒  0 = 36
= 1, ⇒  1 = 37
,  =
∆
∆
=
1
12

= ()

=  +

−
= .
= 49 +
¿  ?
, ()
=0
0 = 49
=2
2 = 51
∆ =
1
51 = 7 +
7
1
1
−1/2 =
= (49 + )
2 49 +
2
¿ (°) ?
= .
= (30°+)
0==0

==1
180
, () = (30° + )
0 = (30°)
1 = (31°)
−   = ∆ . , ()
1
51 −  =  ( )
14
∆ =
−   = ∆ . , ()
1
3
(31°) −
= ( )
2
2
1
3
(
)
31° = +
2
2 180
° = .
° = .
()
= ′()

2 ()
= ′′()
2

()
.
ó
ó
2 ()
.
,    x    ""
3 ()
= ′′′()
3
ó
=  −  +  − ; : ′′′()
′  = 10 4 −12 3 +2
′′  = 40 3 −36 2 +2
′′′() = 120 2 −72
```