Problem 1.1. (40 points) Let
f(x)=4−7
x(1)
(a) Find all the values of xsuch that
|f(x)|<2(2)
and express your answer in interval notation.
(b) Find all xvalues not in the domain of y=(f◦f◦f)(x)[Hint: after finding the expression for
(f◦f◦f)(x)do not simplify it. Just investigate which x’s are not in the domain of the fractions
involved in this expression]
1
-
-
a)
f(x)
=
2
-
If(x))
<
2
*
Isolate
for
x
&
23
4 -
X
-
2
4-
Y
-
4
+Yx
+
4x
-
4
-
6 c
-
/x
2
+
>4
-
2-2
x
D
O
4x
32
X
2
\x14xxTz,
x
ER3
YIz
*
b)
y
=
fof
of
(x)
:.
*
I
FO
:
4
-
:
X
O
=4
-
Fix
*
4-7/x
=
0
=4
-
x
+
44
⑭
,,,
xER3
4
.
IX
-
O
4
-
L
-
Z/X
4
=
=
4
-
Y
4(4-4x)
=
7
28
X
=
16
-
2
=
7
·
-
10
-
10
-
28
-=
-
q
X
=
=
X
