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If \(f:\{1,2,3,4\}\to\{0,1\}\) is defined such that \(f(x)=0\) when \(x\) is even and \(f(x)=1\) when \(x\) is odd, what is the range of \(f\)?

Answer and explanation

Correct answer: \(\{0,1\}\)

By definition, the even inputs \(2\) and \(4\) give \(f(x)=0\), while the odd inputs \(1\) and \(3\) give \(f(x)=1\). Hence, the set of all output values is \(\{0,1\}\). Option D is the domain, not the range. Exam tip: To find a range, evaluate the function at every domain element and list only the distinct output values.

Related tags

Relations-FunctionsRangeParity-FunctionDomain-CodomainReal Valued FunctionsTheir Domain And RangeReal Valued Functions Their Domain And RangeRelations And FunctionsMathematics

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