Given function h defined by $h:\{2,3,4,5\} \to \{7,9,11,12,13\}$

Step1: Checking for Injective or One-One function:

From the given definition of $h=\{(2,7),(3,9),(4,11)(5,13)\}$, we can see that it is one-one, as for every ${2,3,4,5} \in h,\;$ all have distinct images under $h$, i.e., $h(2) \neq h(3) \neq h(4) \neq h(5)$.

Therfore, the function is one-one. We need to now check further for onto.

Step2: Checking for Surjective or On-to:

From the given definition of $h=\{(2,7),(3,9),(4,11)(5,13)\}$, we can see that every element in $\{7,9,11,13\}$ then exists an element $\{2,3,4,5\}$ such that $ h(x)=y$ is onto.

$\rightarrow$ The pre image of 7 is 2 , the pre image of 9 is 3, the pre image of 11 is 4 and pre image of 13 is 5

Therfore, the function is onto as well as one-one and hence is invertible.