To be onto, for any integer y, there exists an integer x such that y = f(x). Give a counterexample, let y = 20, which is an integer. If f(x) = 20, then x = 20 which is not an integer.
To be onto, for any integer y, there exists an integer x such that y = f(x). Give a counterexample, let y = 20, which is an integer. If f(x) = 20, then x = 20 which is not an integer.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.6: Combining Functions
Problem 43PS
Related questions
Question
![To be onto, for any integer y, there exists an integer x
such that y = f(x).
Give a counterexample, let y = 20, which is an
integer. If f(x) = 20, then x =
20
which is
not an integer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F404d1ef0-3316-4381-9a29-8161054821c1%2F9ffa9977-c335-45fb-9cd8-373429f4b95a%2Fa08pnm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To be onto, for any integer y, there exists an integer x
such that y = f(x).
Give a counterexample, let y = 20, which is an
integer. If f(x) = 20, then x =
20
which is
not an integer.
![To be onto, for any real number y, there exists a real
number x such that y = f(x).
Let y be a real number and let x =
Since
is a real number,
must
be a real number.
Hence
is a real number
It follows that f(x) = 2x + 7 =
Since f(x) =
where x is a real number, f is
onto.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F404d1ef0-3316-4381-9a29-8161054821c1%2F9ffa9977-c335-45fb-9cd8-373429f4b95a%2Fwnsyk9a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To be onto, for any real number y, there exists a real
number x such that y = f(x).
Let y be a real number and let x =
Since
is a real number,
must
be a real number.
Hence
is a real number
It follows that f(x) = 2x + 7 =
Since f(x) =
where x is a real number, f is
onto.
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