new doc 1 - mrs. o'farrell's...
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售
役卢
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1 $
启 \ 售•
ダ钿
ダ
デ \一
曾
- B’
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- 1 1 1 1 - B
守朝 わ曾吆
1 B
( 1 1 - 1 1
1 - v I *
1 1 •
专 一勇
歹I 1 1 ム1
9 1
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1 2
- 2 . x
y f r (x ) = x2
+ 4. . y - x
= x , x 0
石百一 1 X I
= + 4 )一 4
T’
(f (x n = T 1
v + 4 )
= x- 4 + 4 = x
== (((16 : - 4 )) 2
+ 4
V e r i i n ggg : f (((& (x )))) = f (((Ji : - 4 )
ff-
. W = J & Hc 2 4
yy = m , x || 44
y 2
= x- 4 , x 2 4
x = y 2
+ 4 , y 0 I n v e r s e
y - / + 4 , x | o
53 f (x ) = x2
+ 4 , x | 0
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一
r 1 1 1 1 1 , x
y , l y æ x
x
V e r i f y i n g :
x
]- ’
(x ) = -
x
xy = - 一
’’
- 3
x = - I n v e Ts e
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/
3
3
3
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3
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3
5/
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f 4
( x ) = x , x ; : 0
T hu s , f (x ) = x , x : : 0
f (x ) = I . , x | o i s o n e - t o -
o n e .
85 . A n s w e r s m a y v a r y . O n e p o s s i b i l i t y f o l l o w s :
in q u a d r a n t I V .
qu a d r a n t I V , w h i c h m e a n s t h e g r a p h o f f
1 l i e
po s i t i v e . T h u s , (b , a ) m u s t b e a p o i n t i n
qu a d r a n t I I , a m u s t b e n eg
a t iv e a n d b m u s t b e
g r a p h o f f
-1
. Si n c e t h e g r a p h o f f l i e s i n
84 . I f (a , b ) i s o n t h e g r a p h o f f t h e n (b , a ) i s o n t h
1ie i n q u a d r a n t I .
(b , a ) a r e p o s i t i v e . T h u s , t h e g r a p h o f fI
m u s
Po s i t i v e , w h i c h m e a n s t h a t b o t h c o o r d i n a t e s o f
q u a d r a n t 1 , b o t h c o o r d i n a t e s o f ( a , b) a r e
g r a p h o f f1
. Si n c e t h e g r a p h o f f’
l i e s i n
83 . I f ( a , b ) i s o n t h e g r a p h o f j , t h e n (b , a ) i s o n t h e
- in g o n th e i n t e r v a l (f (5) , A o) ) •
T 1
(x ) . In a d d t i o n , w e c a n s a y th a t T
’(x ) i s
i s o n e - n e o n t h e i n t e r v a l a n d h a s a n i n v e r s e
s in c e f (x ) is d e c r e a s i n g o n t h e i n t e r v a l (0 , 5) ,
i t
- o n t h e i n t e r v a l (f (0 ) , f (5))厂
’
(x ) . I11 a d d i t i o w e c a n s a y t h a t f-
1
(x ) i s
is o n » n e o n t h e i n t e r v a l a n d h a s a n i n v e r s e
79. s in c e f ( • ) i s i n c r e a s i n g o n t h e i n t e r v a l (0 . 5) , i t
D o m a i n : (0 , 8) R a n g e : [o , 15 ]o f t h e i n v e r s e , w e g e t t h e f o l l o w i n g f o r g
-1
in v e r s e , a n d th e r a n g e o f t h e f u n c t i o n i s t h e d o m a i n
Sin c e t h e d o m a i n o f a f u n c t i o n i s t h e r a n g e o f t h e78.
D o m a i n : [o , o o ) R a n g e : a l l r e a l n u m b e r s
o f t h e i n v e r s e , w e g e t t h e f o l l o w i n g f o r g1
:
in v e r s e , a n d th e r a n g e o f t h e f u n c t i o n i s t h e d o m a i n
Sin c e t h e d o m a i n o f a c t i o n i s t h e r a n g e o f t h e77.
f (x ) =
, O Z × Z r
y 2
. R
2_
x
2
x2
. R2
y
2
x - ww wv • Jr
z x
2
82 f ( x ) = m , 0 [ × [ r
J’
( x ) -
’
(x h ) , m B o
J : .
’
(x h
b . m
y
s e e
0
--
x . Nw
+ h I n v e r s e
> - n ° + h
M ï ( t ) = n ° + h . M + o
S e c t ro n 5 . 2 : O n e - to - O n e F u n c t i o n s ; I n v e r s e F u n c t i o n s
D o m a i n : [5 , o o ) R a n g e : [o ,
- )
o f th e i n v e r s e , w e g e t t h e f o l l o w i n g f o r f1
:
in v e r s e , a n d th e r a n g e o f t h e f u n c t i o n i s t h e d o m a i n
Sin c e t h e d o m a i n o f a f u n c t i o n i s t h e r a n g e o f t h e
D o m a i n : [- 2 , c o ) R a n g e : [5 ,
0 3 )
o f t h e i n v e r s e , w e ge t t h e f o l l o w i n g f o r f1
:
in v e r s e , a n d t h e r a n g e o f t h e f u n c t i o n i s t h e d o m a i n
Sin c e t h e d o m a i n o f a t i 1n c t i o n i s t h e r a n g e o f t h e
in v e r s e .
w b ¢n 虚 ie o u t p u t o f t h e f u n c t i o n i s t h e i n p u t o f
in p 1t o f t h e f u n c t i o n i s t h e o u q p u t o f t h e i n v e r s e
1 & Sin c e g j - 5) = 3 , w e h a v e g’
(3 ) = _ 5 ; t h e
k e i
in pu t o f t h e f u 11c t i o n i s t h e o u t p u t o f t h e i n v e r s ew - 0 u t
& 1 t 0 f e f u n c t i o n i s t h e i n
p u t of
Sin c e f (7 ) = ] 3 , w e h a v e f-
1
(13 ) = 7
; t h e
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pe r ho u r .
t h e s p e e d o f th e c a r w a s r o u gh ly 56 m i l e s
I f t he d i s t a n c e r e q u i r e d t o s t o p w a s 3 0 0 f e e t ,
c r (300) =
6 . 97 • 56 . 0 1
300 + 9 0 . 39
= d
= d + 9 0 . 39 - 9 0 . 39
d ( • (d D = 6 . 97 d
)- 90 . 39
= r
6 . 9 7 6 . 9 7=
6 . 97 r + 9 0 . 39 - 90 . 39 6 . 9 7 r
h r (d (r )) =
6 . 97(6 . 97 r - 90 . 39 ) + 9 0 . 3 9
ó , 97r (d )
l + 9 0 . 39T he r e f o r e ,
w e w o u l d w r i t e69 1
= rl + 9 0 . 39
d + 9 0 3 9 = 6 9 7 r8 7 . = d = 6 . 97 r - 90 . 39
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