I
Algebra 1/Pre AP
Name
Notes - Inverses of Cubic Functions
Date
~~~~
_
Period
_
Definition:
INVERSE OF A FUNCTION: The relation formed when the independent variable is exchanged with the
dependent va riable in a given function. (The inverse may NOT always be a function] ..
Definition:
INVERSE FUNCTION:
If the relation formed when the independent
dependent variable is itself.a function, it is then called an inverse function
EX 1) Graph:
j(X)=X3
variable is exchanged with the
and is noted as j-I
j(x).
Graph the inverse of
X
x
I', f(x)
-,
-2-
-'1
-2-
-I
-I
-I
0
0
I ,
I
r
g
is a reflection of the function over the line y
Is the inverse of any cubic function a function?
=
i.c..(.L(,.c
_hJ
~
Graphtheinverseof
0
I
)..
x .
:.r~ ~ 7;c.,,,u...- .•."'I~ c-:
~
~
c~
~
4 ••.
Z~
3
EX ) Graph the inverse of !fx)=2x -7
~c;{.. ~
I
EX2)
f(x)
-g
0
I
J.
The graph of the inverse of any function
(x) .
j(x)=-(x-4)3-1
f-Jtx )
(-2,-8) (-2.,i) (Z, 7)~(7,2.~
(-1,1)
(0,0)
(o,oJ
(1.1l
(1,-1) (S",-2.)~(-l
(2.,
EX2b) Find the inverse of
f(x)=-(x-4)3-1
(3,o)~(~3 )
(&.I,-tH(-I,,,)
(-1,-1)
g)
(
...,
00>..
(z,-i') ((.,-9)~(..qI
EX 3b)
Find the inverse of
X"= ~'13-7
~=_('j_4)3_1
'K-I-I = - ('} -1/)
~-X-I
.::
.p-'(K)':
3
'J{..J.
7 = 0l!J
l
(~(R
!/-4~X-(
j(x) = 2x3-7
+'4
?A)(+~g
-_
.. ::!:J
~
{-'()e)e
i ~4X+1.8
..J
I
Algebra II Pre AP
Name __
Worksheet - Cubic Inverses A
Date
~
_
Period __
Find the inverse of the following functions algebraicolly.
f(x)=-~(x-7)3_2
2
1)
x= - ~
3
f(x)=(-x+3)3_4
2)
.
I
~:::(T3 ~-+- 3)\3-4
(~-1) 3_~
~+;L == -SJJ. (~-7)
f :/~Lif.J-7)
'X+4=
1
,!X+-£/
(S-O)(4-IOO
If::
I-I(X
l-7
:
X4-lf
4- 4f
-f~=
= 3/2. ':1 4- 3
+
I
(/,5"()X /--100 +
~X+l/
-F- (()();::
z~
y-
-3
~ = ~ erX+-tf
-
--, = (':I -3J
=: V(%.CJ+-3)3
%~=
-# rS-OU/OO
J :: -.:-
3
(~!f+3)
f(x)=-2(x-3)3_4
1C:: -z.(j -3)
3
~X
-f
3)
2
lfx ·HI
3 :::
f -I(X)
- J.
-4
3
~(lj_3)3
--±
!1 :: - ~
- A
3
V"iI)(+-/b
lft.I)c+I~ r 3
=-
ilfZiK+lftJ
.f-3
V
Find and graph the inverse of the following functions.
4)
f(X)=.!:.x3+4
2
5)
-r-'()()
= ¢:ix-i
f-«(x)
- !
!J=)(l
+-(~)
( ::L, iJ
( Z-,I.{)
(
(',')
.(I,~)
(I, ,,~)
(0,0)
(0)0)
(0,£1)
(-',-1)
(-I,-'1-d
(-2.,-8)
(-J./-I./)
z., i)
~ ( ~/1.)
~(L{~/O
-') (4 I 0)
(-1,3 yz) 4 (3 ~ -I)
I
(-2.,0)
f(x)=-(~"-+-1)3_:t
~(o
-1.)
I
6)
'C-~.
V)(+.:t -3
f(x)=(x-4)3+2
f-rx)
= ~x-i +4