Solutions to Quiz 16A
www.math.ufl.edu/˜harringt
November 26, 2007
1. Use the chart to answer the following questions.
x
0
1
2
3
f(x)
1
0
3
2
g(x)
3
1
0
2
(a) (
f
◦
g
)(2) =
f
(
g
(2)) =
f
(0) = 1
(b) (
g
◦
f
)(2) =
g
(
f
(2)) =
g
(3) = 2
(c) (
g
◦
g
)(3) =
g
(
g
(3)) =
g
(2) = 0
2. Please find two functions
f
and
g
such that (
f
◦
g
)(
x
) =
1
√
x
2
+1
.
I would like to point out that the solution is NOT unique, meaning
there are different answers one could give and still be correct.
One possible solution:
Let
f
(
x
) =
1
√
x
and
g
(
x
) =
x
2
+ 1
Another possible solution:
Let
f
(
x
) =
1
x
and
g
(
x
) =
√
x
2
+ 1
Other solutions may exists. The only solutions that will not be accepted
are the
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 Fall '08
 WILLIAMSON
 Math, Calculus, Algebra, Semiotics, Following, possible solution

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