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Subjects
Class 12MathematicsRelations and FunctionsIntroduction to RelationsMedium
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If (f(x)=|x-5|), what is the set (f^{-1}({3}))?

Answer and explanation

Correct answer: ({2,8})

Step 1: To find the preimage, solve (|x-5|=3). Step 2: This gives (x-5=3) or (x-5=-3). Step 3: Hence (x=8) or (x=2), so the preimage is ({2,8}).

Related tags

PreimageAbsolute ValueFunction Inverse ImageIntroduction To RelationsRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1If (A={1,2}), what does a relation on (A) mean?
  2. 2If (A={a,b}) and (B={1,2}), how many ordered pairs are there in (A\times B)?
  3. 3If (A={1,2}), how many total relations can be formed on (A)?
  4. 4Which relation is the universal relation on (A={1,2,3})?
  5. 5Which statement is correct about the empty relation?
  6. 6If (A={1,2,3}), how many pairs are there in the universal relation on (A)?
  7. 7Which pairs are compulsory in the identity relation on a set (A)?
  8. 8If (A={1,2,3}), which is the identity relation?
  9. 9What condition is necessary for a relation (R) to be reflexive?
  10. 10On (A={1,2}), which property is definitely satisfied by (R={(1,1),(2,2),(1,2)})?
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