© 2017 R. Boerner, ASU School of Mathematical and Statistical Sciences.
This solution is licensed to ASU students registered for MAT 243
classes for free personal use. It is not to be uploaded to third-party websites, especially not ones that sell such unlicensed content. If you
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MAT 243 Online Written Homework
Assignments for Week 6/15
1.
Are the two functions
?
and
?
defined by
?: {0,1} → {0,1}; ?(?) = ?
2
?: {0,1} → {0,1}; ?(?) = ?
equal or not equal? Explain.
?
and
?
are equal. Their domain and codomain are equal and
?(?) = ?(?)
for ALL
?
in the
common domain, since
?(0) = ?(0) = 0
and
?(1) = ?(1) = 1.
2.
Is the function
?: [0,1] → [1,5]; ?(?) = 4? + 1
bijective? Prove or disprove.
Proof:
.
3.
Is the function
?: [−1,1] → [0,1]; ?(?) = ?
2
bijective? Prove or disprove.
2
.
4.
Prove or disprove: the floor function is additive, i.e. whenever
?
and
.
5.
Find all real solutions
?
of the equation
⌊2? − 1⌋ = 5
. Show your work. Give your solution
set as an interval.
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© 2017 R. Boerner, ASU School of Mathematical and Statistical Sciences.
This solution is licensed to ASU students registered for MAT 243
classes for free personal use. It is not to be uploaded to third-party websites, especially not ones that sell such unlicensed content. If you
found this document on a third-party website such as Course Hero or Chegg, the document is being served to you in violation of
copyright law.
.