The oneover (reciprocal) function will be the
function defined by
F(x) =
1
x
.
1.
What is the domain of F?
2.
For what values of x is (F°F)(x) = x?
3.
Construct an extension G of F such that (G°G)(x) = x for all x ∈ R.
4.
Construct some slight modifications H1, ... of F such
that (H.°H.)(x) = x for all x ∈ R.
5.
Think of some continuous functions C(x) such that
(C°C)(x) = x for all x ∈ R.
Problems from Spivak - Turn in September 26, 2007 as
Problem Set 04.
1.
Chapter 3, Problems 4 and 5
2.
Chapter 3, Problem 10
Descriptions of Graphs
Draw the graph of a (not too complicated) function f. Write down
a description (complete sentences) of the graph including
information about intervals of continuity, monotonicity, and
concavity and the values of f(x) at not more than four points.
Pass the description only to your neighbor to draw the
graph. Compare your neighbor's graph with your own and discuss.
Repeat!
Group Version
As a group, draw the graph of a (not too complicated) function
f. Write down a description (complete sentences) of the graph
including information about intervals of continuity, monotonicity,
and concavity and the values of f(x) at not more than four
points. Pass the description only to another group to draw
the graph. Compare the other group's graph with your own and
discuss.
Repeat!
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