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Class 11MathematicsRelations and FunctionsFunctions as a special kind of relationEasy
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If the function \(f=\{(1,1),(2,8),(3,27)\}\), which rule is correct for the given input values?

Answer and explanation

Correct answer: \(f(x)=x^3\)

The function gives \(1\mapsto1\), \(2\mapsto8\), and \(3\mapsto27\). These outputs are respectively \(1^3, 2^3\), and \(3^3\), so the correct rule is \(f(x)=x^3\). For instance, \(f(x)=x^2\) would give \(f(2)=4\), so option B is incorrect. Exam tip: test the proposed rule with all the ordered pairs, not just one pair.

Related tags

FunctionsRelationsRule IdentificationCubic FunctionOrdered PairsFunctions As A Special Kind Of RelationRelations And FunctionsMathematics
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10 more MCQs
  1. 1When is a relation from (A) to (B) called a function?
  2. 2If \(A=\{1,2\}\) and \(B=\{3,4\}\), which of the following relations from \(A\) to \(B\) is a function?
  3. 3Why is R = {(1,2), (1,3), (2,4)} not a function from A = {1,2} to B = {2,3,4}?
  4. 4If (A={a,b,c}) and (R={(a,1),(b,1),(c,2)}), which statement about (R) is correct?
  5. 5Which of the following statements is always true for a function?
  6. 6If \(f:A\to B\) is a function, what is \(B\) called?
  7. 7If \(g(x)=2x\) and \(A=\{1,3,5\}\), what is the value of \(g(3)\)?
  8. 8Which mapping idea correctly identifies a function?
  9. 9If a relation from the set A={1,2,3} to the set B={a,b} is given by 1→a, 2→a, and 3→b, what type of relation is it?
  10. 10If A = {1, 2, 3} and R = {(1, 2), (2, 3)} is a relation, why is R not a function from A to A?
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