Topic 5

S**1 7 ffi,xffirf,*gmg

Sirrrpllry the followins.

,{XT'4Ysy4 ?"1 {q

de sf

q wZ -L4J - r rt rrr

az-

5. X-e {- 3Z,

A. aLb{ h co?ecrdef

6. TL q s{LI

(3 uL

141 X3 yx

r$S *-*ar f3u tuT

*apqt

tqL 3qr Lpr

,'XY3 *t* **r;z7e

/. fn + aq r ?q, Z. !.t,=..hLzo ^ zoy 6f trJ

Sue^t

Topic 5

Ansr'vers an Psge 368I

-.:.

as'r,nuch'fi$ p*snible. : :

': H ,, frS+,3h_""6C+4b".*"lf;#**fJ

Simpfify the fcllowing equatinns

|f; Spq+4qP* I2563 t-.tyxi5r*s l

$ {'= 3#i{ *5b} ffi *7 {{ 3o 7cI{

;Tb *'*4

s yx:::: 174e 6ed

's,i 3a 6tt ,;-"--1u '! :4b '- ldflbc

* |

fvlultipfy out the hrack*ts.

pqx 4r "{"- }p * qr * 5

*s{*?f} x 3u{*Y} * 13

t*3r)

t4ts

I

Tffi

tr*3fr

followi ng expressions.

ffi 13{*"4p}{*2q}2a 4c

x -**-* ::-5b 10sxv xz._1 ". _l*"--:- ywz wv

3{?r * 3d}q

5xty2 * 13 i

tw+xi{y+z!tf;m-3nltn+rn)*3{ Lxn 0}{# * u?}

ts

$tr

t3 2{a + 2b!

15 *3 izp - qi

I7 _2q( 3p3 rils tk * /)tl * k)

At {44 * 3b}{3b"-: 2*}

Rern*ve the brackets fram the

33 5{3*x{,4*}r}}e4 plq{,r *- 3t * p}

?5 2{a( tu-*3} 5} 6a

f,S 2lx * x{x + 4{2 + x}}:

2V 3ia *- 3{3tZ ". bi * 2}:

e8 4{s + ls * 3}{5 -i- 2}}

2g 2ti? + x)t2 * x) -+- {x - 3;tx -,- 3}}

3* k[2{3{Ir+2}+ f } * 4{10*s{fi+ t}}i

Simpllfy the followi,ng expreEsinns a$ much fr$ poqsibh

3$ -t*3".f-4c 3r

sd 93*ry*' eb ad3s #-#

2, ZarG o,- *3 $+ 4b-Lc*2* s/6**]b*8c=/

ba32 ^ -t -l-rtu 3qx 4px

rF xz zJ556ry3

ta

?? I JJJ khk

I 5rr +*p,/,

P7

G6?ts-/?

9r?I

SueL

Topic 5

&A B Rwrs ic-r^- ( cn^-{ ,o( )

1r'4,'6.x rc52'glq Vt l6L

*1'-=9

3, *{x ,J" : *7c/fa/6 s *7g-

z/' (

t4r 3n - *bt7c6a*:7 be

Iryx&:tT4e EdL

Beut.flu,'$t x'fuW =/-fet &L

I h 2Jt : I

+.3, hru, + 372r; 5l2*rf,

6,

8.

5.

7.

2s{ ,_/ lo

*3f8rz

-7hv s t3

s-/{,tA/; 13

: 13

I.I

lo. Eu, x k, j /*5b F+J-

f =17 4furL. {5. x yd: v

yre ye3' :vreL-

t3, 2a*#4b t+,6c -2cI t5-6p * 3L

/6 3'- 5nZ3 t7. * 6ftt + Zf , /9, y *uta *:i rx--z

19. - ( kh. ()L zo, \vtn *Zt4>*3hz,,-p 3qru

= *fukL * Zk(- *IL

z- l. *arl. - 8 o,L '9 bL + 6o-l

= .- BaL e/B"rb Y) 9 L'

zg. S[s + Lv**JJ: tf * 2nx+fccy

= 7mL * hh -3n>

zL, -3 [z*{2'*X1+ r]* 6 eA +3 e*-** 9 o-*

a'

*e sl

r{Lr*sfl-fj= p7r b3f?-*f>

z+.

Sue-t

Topic 5

&L 0 Rw (***trL)zf.Lt0,,b +3a-*fJ-(ou ;:6,2[rr+?c{**8"+*I]

= 2^/b *lf = Z[rc +-fx">* S*J*. tofuL*l8x

zZ, 3l & r3t 6 +3b -rjJ zB, +f$ *s2-*s *LJ

{ 3[o+9b *rzJ s 4s'* Z#

: 3a* $Tlb $36

zq, z{4-T,b +rcL-9J 3a. kI z{3k*6.4-4{,r*{k-4Ja kl 6k+ lL +zqt<* /6 1

= SakL

gz. !!-e. ! l?,?l2 p?-fr*

b, Y' lO

31. 30,+ B*ILC

: lla,-l2c

"? Lrt' * i{ J ) ,. . 't'-

l- k*

57

34' #?:-!r,a-b cr(

SueL

Topic 6

9-03 ffixffirtr$sms

rite the functions described belnw. ln each case the input is x.

T Multiply the input by 4 and then add 3

tr Add 4 to the input and then multiply the result by 3

3 Multiply the input by 3, dlvide the result by 2 and subtract 5

4 Square the input, then multiply by 5, then subtract the input

5 Multiply the input by 2, add 3 and then find the square ront of the result

S Subtract 6 from the input, square the result, subtract 3 and square raot the result

Write the process defined by each of the following functions.

f ftx| .6x-t-2 {$ fix} =5ix*3}

# fixi ...'':.4S t# f{xi ::Sx3 r'i"$ T f i, X | :::.: 1'rl; :l 4

/. ft*): 4n+3

4, f u): fircL- x-

2, {r*l: 3 (n + +) 3.

f,* s 6,frrq:

fc"ls3x- €T_J

5.

7.

B,9.

/o.

/t .

/2.

h'G)L-3

,/"{u#!rtL inf *} * 6, ad.& 2

3'tt i"yn{, mr^,ffyy 4f4eft1 inf*l b,J 2/ divlle Lff.f) a/"(+h6; iop*/, **fry1 bJ 6 / au'6lru

/,f&f * in f/ b,J"3-, aafu(4rlotr*n c.4be roo/

5?f o( rc re*{ ,nf }, s,*b/*oo} t **tre s4c,l{< r'-/,s;hhorfZ) syc&{vsu/f,{.

I

I

I

L

Sue^L

Topic 6

9-06 ffimtrrn$sms

Evaluate the functions when xt the input, tfikes the value of 2.

1 ftx] -- 5x * 3 H f{xi -* 4{x +' 6} 3 f lx}

d f txi -, 3x2 5x 5 f(xJ '.,,, o,'ffi + f S fix)

Evaluate the function f ix, + 3 for:L

r fi3] ffi f(5) s ft10)

lf ftx) ; 3xr -* x what are:

l# f{a^2} $"$ f(3b 2\ .gtr ftcz\

/.

4.

7.

z. +(z+() =JLfxZ

3 rZL- f*Z 5.

fxf -3 ?L

fr/C3 :

3( 3b -L)L* ( lb*L)

3

slz -- 5

Answer$ sn poge 97

5x':: **--*

2I

7

:l=

-g: 2:f Wr:z

z3.

6

AJIL

-E-

I-

lq x2 +z

B,

9

5 x] _

z

fxlo z:22'FJ

2

3(qrz)L- (a4z)3 (aL +4a*+) * dt* e L3a' + lla- Ha

2" 3 (c')' 'iF cL

: 3c +-c>

10.

ri

.F

IIll,

: 3(9bL - {2b++) *3b+L

: 21 bz49b + /#

Sue-t.

Topic 6

$*SP Hxerfrfrs*s

Write the functicns defin*d bel*w, where ftx] ** 4x * 3, S{x} * ?x? and h{x} *,x + 5. '

t f{g{x}} 3 gtf{xi} 3 fthlx))

4 hlftx]) $ S{h{x}} 6 ht g{x i}

l^ {tti'): 4x(m"4 -3 2r 3 ( +?L*3) " :^(4,2 -,1'

Bnt' * J

3. {f ?c+t = 1(t*s) -3 4. h14x-i) = 4?r--3 tf

5, 3(rc+Y). Z(^x-*dL

? Z,rcL *zot.+fo

Sue.t

Topic 6

9-I 4 ffix*tr-ilfrs*s

By plotting a graph, where appropriate, estimate the range of

1 Y frx) 6x * 20 in the domain 2 {"-: x * 3

tr y f lx) ,, x2 -i 3 in the domain -5 :'; x :; 5

.$ y::: f t x) , , *1*r in the domain 3 ,';- x '':- 0x -,-- 4

4 Y::;. ftXi -': X3 i xz X *- 1 in the dOrnain 1.1 "::" x, "'' S.4

S y.=ftxl ,=,xz inthedomain -1 :ix':::1

S y::ftxi" -I,inthedomain 1'::x.:. 2x1

the follawing functions.

/. 6r'2(x3

6,xO

F-f (-L)

{r b)

f (e)-L

i'| Zo*2o

b

,,,

3 *32

-flbttt &^

= -Zo

L3

(r)L+SL+j

o L + 3

SsZP2.

*28fG5frr)f,o)

):

-- =3

('rzs) ({,zg)

Qt

*tz(3{..} -} -Z-l

( o r\)

r I 1 ? f

2B3 (v4'

g, {t*3)3

d

J3 +$

-2

-'b' +, f (-

frol, l)

.4)

s (- t. l)''+(-t.l)\(-t.t)*l: n l.r?l ; l.Zl +l,l * I sb" olla (o.+l l + (o.4)L -(o.+) - |: o.o6++O,lL *O.+-l a*1.| ( o) = *-: o'25

-+ *)

0,lt'$

ttl

'(o;o.zr)

".?, * |

5(lNfUJ

Sue^t

*LoI-/

1o-r?)

Topic6

9. l+ ( *nl'&)

fr*t){rn )

rv)

-l= (-t) = I

= ( l)*t. I

-)&

6 f (-'r)

+ (z)

{(o)=

fi ..1*l-

g nl -l

?,J"*2*l-l

=*) 7r.

al

{(t) )m

fq) =f{-t-+ IfF

b,t)'t t ,

(*lr-L

rl:

I

I

h( o, *l)

Suef.

Topic 6

9*16 ffix*r#lsffi$

state, for each of the following whether it is

function. Also state any n*cessary excluslons ts

1 f *3x-+-2 3 f:::":3";+24 Y*:3x*1 '*? s Yffi3x;+?

a n'lnny*to-onethe dcmain.

3

s

function or a sne*ts*s

Y * 3x3 +-2

!,/ :.' 3X* 3 -+ ?

,.$

H

*$'#

s$.q

':i#: f:*

.:r?

"$

.$

0. rl

l. slrorL'ql'nt Itnuon€- h.ouone--

4.*+o

on'e 4"o^e

-l Ir =fr

L, pa,w.bola*rna"X l" o ne'--

*Z* |{. n fiz-x*# o

P4\ut"'6f4f h e'"?-

d**L *(.K)1" (*li>

6. t*3= *L{a

otvt h one

SueL

\ffrite,r$

f

&r.+

V/hatp

p{

t\$_d

the functions using f {x} -* 5x I 7, g{xi ::::;:: x; -i-

ftgtxlj tr gtfix)lhl frxlt h gthi xii

is the range of the following functions?

y ftxi,,-,,' 5x *- 3 in the domain - 3 { x $ 3

y i:::j fix| -; 2x2'i-- 7 in the domain --2 S; x 3, 3

y T::: f lx1 ,,-, -i- in th* damain I .:!,x:i 22x -.- 3

y;:: f txl -* l*' -i xz -r x *- 3 in the domain 3 {: x { 33

y:: ftx) ,,, x 3 in the domain 2 t:l x d- 1

y:-, f{x} , *-1*" in the domain Lr'i- x ::; 12x-3

Answers #r1 page 3 69

1 and htx| ,-, ,Y3 i 2,

3 fi,ht xliS htg( xii

3-z r3

sJ*+*3

Topic 6

T#

.S .{

{$

Tff

2.3(5n+7)/. {( frz+r ) : f( nLet) t75x'+ lL5(x5*L) *7frt?+tT(r.rn4 L+

|

LL *4zJ +t

4, A(fr*Z)3, .f(rst, i=

J

7.

{, 3(rt nq =

:

6. L(fL+r) : kL*t)' + L? x6+3r*+ 3r-> +3

lrL{

S'r.{ zro

L+

*j.g

*l

-J.1

a tLf 2.7 + fZf*t+ 73ft-319:

slro,;o l"l' lf,*c-F(*t)u* -5x3*5 = "16)t{(il r {tr3-3 atL

*tg bc $ tL

S" fa(^bo{r.-{r'a) s /x + *7 :3

f ( 3) r zr917 B'

frol = 77

9, {r,){r>)x_

I/1

; +lI

aI Jt*

7

ts. { f* l):f(3):

ll. {(-zf (*l

{(*L

{(,)

):

);

)=

{ -3/,

{ec( I

t?_.

x *lSue^C