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Let \mathrm{A=\{1,2,3,5,8,9\}}. Then the number of possible functions \mathrm{f: A \rightarrow A} such that \mathrm{f(m \cdot n)=f(m)}.\mathrm{\mathrm{f}(\mathrm{n})} for every \mathrm{m, n \in A} with \mathrm{m \cdot n \in A} is equal to _______.

Option: 1

1


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

LHL                                                           RHL
\mathrm{\lim _{h \rightarrow 0} g(H(1-h-1))}                   \mathrm{\lim _{h \rightarrow 0} g(H(1+h-1))} 
\mathrm{\lim _{h \rightarrow 0} g(2(-1)-f(-h))}                \mathrm{\lim _{h \rightarrow 0} g(H(h))}
\mathrm{\lim _{h \rightarrow 0} g\left(-2-\frac{1-h}{|-h|}\right)}               \mathrm{\Rightarrow \lim _{h \rightarrow 0} g(2(0)+(h))}
\mathrm{\Rightarrow \mathrm{g}\left(-2-\frac{-1}{1}\right) }                         \mathrm{g(0-1) }
\mathrm{\Rightarrow 2(-1)=+1 }                            \mathrm{\Rightarrow 1 }

\mathrm{\therefore \lim _{\mathrm{h} \rightarrow 0} \mathrm{~g}(\mathrm{H}(\mathrm{x}-1)=1 }
    

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