State with reason whether the following function has an inverse: $f: \{1,2,3,4\} \rightarrow \{10\}$ with $f = \{(1,10), (2,10), (3,10), (4,10)\}$.

(D) The function $f: \{1,2,3,4\} \rightarrow \{10\}$ is defined as $f = \{(1,10), (2,10), (3,10), (4,10)\}$.
From the given definition of $f$,we observe that $f(1) = f(2) = f(3) = f(4) = 10$.
Since multiple elements in the domain map to the same element in the codomain,$f$ is a many-one function.
Therefore,$f$ is not one-one (injective).
$A$ function has an inverse if and only if it is bijective (both one-one and onto).
Since $f$ is not one-one,it does not have an inverse.