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If \(y=|x+2|-|x-2|\) and \(x>2\), what is the value of \(y\)?

Answer and explanation

Correct answer: 4

When \(x>2\), both \(x+2\) and \(x-2\) are positive. Hence, \(|x+2|=x+2\) and \(|x-2|=x-2\), so \(y=(x+2)-(x-2)=4\). The option \(2x\) results from mishandling the subtraction of the second modulus term. Exam tip: determine the sign of each expression inside an absolute value before removing the modulus.

Related tags

GraphsAbsolute ValuePiecewise FunctionsRelations And FunctionsReal Valued FunctionsTheir Domain And RangeReal Valued Functions Their Domain And RangeMathematicsClass 11 Mcq

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