Mathematics - Functions Question with Solution | TestHub

$\begin{array}{rl}& A=\{1,2,3,4\}\\ & B=\{1,4,9,16\}\end{array}$

Total number of functions $=4^4$
Total number of one-one functions $=4!$
Total number of many one functions $=4^4-4!=232$
Total number of many-one functions in which $1\notin f(A)=3\times 3\times 3\times 3=81$
$\therefore$ Total number of many one functions $1\notin f(A)$
$\begin{array}{rl}& =232-81\\ & =151\end{array}$