MATH 1500 D01/D02 Fall 2015 Assignment 1
SHOW ALL WORK to get full marks. Leave answers as exact answers. For example,
leave it as 1
{
7 as opposed to 0
.
142857
.
Word problems should have sentence answers with
units. This assignment covers sections 1.1, 1.3, 1.5, 1.6, 2.1, 2.2, and 2.3.
1. For the following functions, simplify
f
p
a
`
h
q ´
f
p
a
q
h
as much as possible.
(a)
[4]
f
p
x
q “
x
2
`
6
x
´
4
(b)
[4]
f
p
x
q “
x
`
1
x
´
1
2. For the function
f
defined by
f
p
x
q “
x
2
´
3 :
(a)
[3]
Find an interval (as large as possible) such that
f
is one–to–one.
(b)
[4]
Find the inverse of
f
on the interval from part (a).
(c)
[3]
State the domain and range of
f
and
f
´
1
using the restriction from part (a).
3. Solve the following equations.
(a)
[4]
log
3
x
`
log
3
p
2
x
`
1
q “
1
(b)
[5]
`
3
?
2
˘
x
`
10
“
2
x
2
(c)
[3]
e
x
2
e
x
`
6
“
1
4.
(a)
[4]
Sketch the graph
f
p
x
q “
$
&
%
p
x
`
1
q
2
x
ă ´
1
´
x
´
1
ď
x
ă
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 Fall '10
 ThomasKucera
 Math, Calculus

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