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Class 12 Relations And Functions · Assertion Reason1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Assertion Reason #62

Assertion: For \(A=\{-1,1,2,3\}\), \(B=\{1,4,9\}\) and \(f:A\to B\), \(f(x)=x^2\), the function is many-one. Reason: If \(x_1\ne x_2\Rightarrow f(x_1)\ne f(x_2)\) for every pair of domain elements, the function is one-one; otherwise it is many-one.

✅ Step-by-Step Solution

Final Answer: Option (A): Both Assertion and Reason are correct, and the Reason is the correct explanation of the Assertion.
  1. The distinct inputs -1 and 1 both map to 1. Thus the function fails the injectivity criterion in the Reason and is many-one.

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