Time allowed: 15 minutes.
1. (2 marks)
On the same axes, sketch the graphs of
y
=

2
x
−
7

and
y
= 3
x
−
2.
Hence, or otherwise, solve

2
x
−
7

= 3
x
−
2.
2. (2 marks)
Show that
f
(
x
) =
x
3
+ 6
x
2
+ 15
x
+ 3 has an inverse function.
3. (4 marks)
Determine
a, b, c, d
such that sin
π
8
=
a
+
b
√
2 and cos
π
8
=
c
+
d
√
2.
4. (2 marks)
Find
d
dx
cosh(sin
x
).
Week 3
Tuesday 1011 Class
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