State with reason whether following functions have inverse $f: \{1,2,3,4\}\rightarrow\{10\}$ with $f =\{(1,10),(2,10),(3,10),(4,10)\}$
State with reason whether following functions have inverse $f: \{1,2,3,4\}\rightarrow\{10\}$ with $f =\{(1,10),(2,10),(3,10),(4,10)\}$
$f :\{1,2,3,4\} \rightarrow\{10\}$ defined as $f =\{(1,10),(2,10),(3,10),(4,10)\}$
From the given definition of $f$, we can see that $f$ is a many one function as
$f(1)=f(2)=f(3)=f(4)=10$
$\therefore f$ is not one - one.
Hence, function $f$ does not have an inverse.
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