128 Surds, indices, and exponentials (Chapter 4)

10 Expand and simplify:

a ex(e¡x+ex) b (2x+5)^2 c (x

1

(^2) ¡7)(x
1
(^2) +7)
11 Solve forx:
a 6 £ 2 x= 192 b 4 £(^13 )x= 324
12 Solve forxwithout using a calculator:
a 4 x+1=
¡ 1
8
¢x
b
25 x
5 x¡^3

5 x
125 x¡^2
c
3 x+2
93 ¡x

271 ¡^2 x
32 x
13 Suppose f(x)=2¡x+1.
a Find f(^12 ). b Findasuch that f(a)=3.
14 On the same set of axes draw the graphs of y=2x and y=2x¡ 4. Include on your graph
they-intercept and the equation of the horizontal asymptote of each function.
15 Consider y=3x¡ 5.
a Findywhen x=0,§ 1 ,§ 2. b Discussyas x!§1.
c Sketch the graph of y=3x¡ 5. d State the range of the function.
16 Consider f:x 7 !e^2 x¡^1 and g:x 7 !e
p
2 x.
a State the range off.
b Find the exact value of g(
p
2).
c Solve f(x)=g(x), giving your answer in the form x=a+b
p
2 where a,b 2 Q.
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\128CamAdd_04.cdr Tuesday, 14 January 2014 10:29:10 AM BRIAN