Whether f is a function from Z to R if&nbsp;a)&nbsp;f(n)=±n.&nbsp;b)&nbsp;f(n)=n2+1.&nbsp;c)&nbsp;f(n)=1n2−4.

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Whether f is a function from Z to R if&amp;nbsp;a)&amp;nbsp;f(n)=±n.&amp;nbsp;b)&amp;nbsp;f(n)=n2+1.&amp;nbsp;c)&amp;nbsp;f(n)=1n2−4.

SaurbHurbkj · Accepted Answer

Definitions&amp;nbsp;Each element of A has been assigned to exactly one element of B in a function from A to B.Solution&amp;nbsp;A=Z&amp;nbsp;B=R&amp;nbsp;a) Given:&amp;nbsp;f(x)=±n&amp;nbsp;f is not a function, because every element&amp;nbsp;x∈Z&amp;nbsp;(except for&amp;nbsp;x=0) has been assigned to more than one value.&amp;nbsp;For example: if&amp;nbsp;x=2, then&amp;nbsp;f(x)=2&amp;nbsp;and&amp;nbsp;f(x)=−2. When x = 0, a function should only have one value for f(x).b) Given&amp;nbsp;f(n)=n2+1&amp;nbsp;f is defined for all&amp;nbsp;n∈Z&amp;nbsp;and the function f maps every element of&amp;nbsp;Z&amp;nbsp;to exactly one element in&amp;nbsp;R, thus f is a function.&amp;nbsp;c) Given:&amp;nbsp;f(n)=1n2−4&amp;nbsp;We note that at n=2 or n=-2, the function is not defined, because we cannot divide by 0. As a result, f cannot divide by 0. This then means that f cannot be a function from&amp;nbsp;Z&amp;nbsp;to&amp;nbsp;R, since&amp;nbsp;2∈Z&amp;nbsp;and&amp;nbsp;−2∈Z&amp;nbsp;n2−4=(±2)2−2=2−2=0

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

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