Lecture Note Function
(Suppose the total cost of manufacturing q units of a certain commodity is given by the
function. a. Compute the cost of manufacturing 20
units. b. Compute the cost of manufacturing the 20th unit.) (Answer: a. $4,500 b. $371)Cq q()=− + +^3230 q 400 q 5004 rkGnuKmn_bNþak; (Find the composite function)ghx⎡⎣ ( )⎤⎦
a.g(uu)=+ =−^2 4,hxx( ) 1
b.gu()=+−326,u^2 u hx x( )=+ 21
c. () ( ) ()
(^32)
gu=−+u12,u hx x=+
d. () 2 ()
1
gu ,1hx x
u==−
e. (^) ()^2 ()
1
,
1
gu u hx
x==
−
5 rkGnuKmn_bNþak;tamkarbBa¢ak;dUcxageRkam (find the indicated composite function)
a. fx() ()+=1 wherefx x^2 + 5
b.f() ()x−=2 where f xxx 22 −+3 1
c. () ()()
(^52)
f xfxx−=+1 where 1 − 3 x
d. ()
12
ffx where 3 x
x x⎛⎞ =+
⎜⎟
⎝⎠
e.f()xx^2 +− 3 1 where fx( )=x
d. () ()
1
1 where
x
fx fx
x−
+=
6 rkGnuKmn_ hx()nig g()u Edl f(xghx)= ⎡⎣ ( )⎤⎦
a. ()() b.
523
fx=−+x 312 x fx( )=^35 x−^
c. ()()() d.
2
fx=−+ −+x12 1x (^3) ()
()
3
1
4
4
fx x
x=+−
+
e. ()
()
31
3
4
fx x
x=+−
+
7 enAkñúgeragcRkmYy éføedImsrubelIkarplit ÉktakñúgkMlugénsgVak;plitkmμRbcaMéf¶ KW
duløa. kñúgmYyéf¶ brimaNplitpl
qCq q q()=++^2900 qt( )= 25 tÉktaRtUv)anplit
kñúgry³ eBl tdMbUgénExSsgVak;plitkmμ. k> cUrsresr éføedImsrubelIkarplitCaGnuKmn_ént.
x> etInwgRtUv cMNayb:unμanelIplitkmμ enAcugem:agTI3? K> etIenAeBlNaEdléføedImsrubelIkar
plitmandl; $1? (At a certain factory, the total cost of manufacturing q units
during the daily production run is1, 000
Cq( )=+q q^2 + 900 dollars. On a typical
workday, units are manufactured during the first t hours of a
production run. a. Express the total manufacturing cost as a function of t. b.How
much will have been spent on production by the end of the 3rd hour?) c. When will
the total manufacturing cost reach $11,000?qt()= 25 t