JEE Mains · Maths · STD 12 - 1. relation and function
Consider two sets \(A =\{ x \in z :|(| x -3|-3)| \leq 1\}\) and \(B=\left\{x \in R -\{1,2\}: \frac{(x-2)(x-4)}{x-1} \log _e(|x-2|)=0\right\}\). Then the number of onto functions \( f:A\rightarrow B \) is equal to:
- A 62
- B 79
- C 32
- D 81
Answer & Solution
Correct Answer
(A) 62
Step-by-step Solution
Detailed explanation
\( A:||x-3|-3|\le1 \Rightarrow -1\le|x-3|-3\le1 \) \( 2\le|x-3|\le4 \) \( 2\le(x-3)\le4 \) or \( -4\le(x-3)\le-2 \) \( 5\le x\le7 \) or \( -1\le x\le 1 \) \( A=\{-1,0,1,5,6,7\} \) \( B \Rightarrow x=4, |x-2|=1 \Rightarrow x=3 \) or \( 1 \) (reject) \( B=\{3,4\} \) Number of onto…
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