Consider two sets $A = \{ x \in z:|(|x - 3| - 3)| \leq 1\}$ and $B = \left\{ x \in \mathbb{R} - \{ 1

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Consider two sets $A = \{ x \in z:|(|x - 3| - 3)| \leq 1\}$ and $B = \left\{ x \in \mathbb{R} - \{ 1,2\}:\frac{(x - 2)(x - 4)}{x - 1}\log_{e}(|x - 2|) = 0 \right\}$.

Then the number of onto functions $f:A \rightarrow B$ is equal to :

Accepted Answer

A : $||x - 3| - 3| \leq 1$$${\Rightarrow - 1 \leq |x - 3| - 3 \leq 1 }{2 \leq |x - 3| \leq 4 }$$$2 \leq (x - 3) \leq 4$ or $- 4 \leq (x - 3) \leq - 2$$5 \leq x \leq 7\ $ or $- 1 \leq x \leq 1$$$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 functions from A to $B = 2^{6} - 2 = 62$

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