Determine whether f is a function from Z to R if a) f(n) = \pm n. NS

LoomiTymnk63x

LoomiTymnk63x

Answered question

2023-03-29

Whether f is a function from Z to R if 
a) f(n)=±n
b) f(n)=n2+1
c) f(n)=1n24.

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Answer & Explanation

rangiranitlh9

rangiranitlh9

Beginner2023-03-30Added 6 answers

Let's examine each function to determine if it is a function from Z (integers) to R (real numbers).
a) f(n)=±n:
This function is not well-defined since it does not specify whether it should output +n or n for each input n. For example, if we take n=1, it is unclear whether f(1) should be +1 or 1. Therefore, function f is not a function from Z to R.
b) f(n)=n2+1:
For any integer n, the expression n2+1 is always a non-negative number. The square root of a non-negative real number is a real number. Therefore, the function f(n) is well-defined for all integers n, and it is a function from Z to R.
c) f(n)=1n24:
This function is not well-defined for certain integers. Specifically, when the denominator n24 becomes zero, the function is undefined. In this case, when n=2 or n=2, the denominator becomes zero, resulting in a division by zero error. Therefore, the function f(n) is not a function from Z to R.
In summary:
a) The function f(n)=±n is not a function from Z to R.
b) The function f(n)=n2+1 is a function from Z to R.
c) The function f(n)=1n24 is not a function from Z to R.

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