The problem asks whether the function defined by the table has an inverse. The table gives the values of $f(x)$ for $x=1, 2, 3, 4, 5$.

1. Problem Description

The problem asks whether the function defined by the table has an inverse. The table gives the values of $f(x)$ for $x=1, 2, 3, 4, 5$.

2. Solution Steps

A function has an inverse if and only if it is one-to-one (injective). A function is one-to-one if each element in the range is associated with exactly one element in the domain. In other words, for a function to have an inverse, $f(x_1) = f(x_2)$ only if $x_1 = x_2$. We can test if a function has an inverse via the horizontal line test. If any horizontal line intersects the graph of the function more than once, then the function does not have an inverse.

In this problem, we are given the function as a table of values. If there exist values $x_1$ and $x_2$ such that $x_1 \neq x_2$ but $f(x_1) = f(x_2)$, then the function is not one-to-one and therefore does not have an inverse.

We have $f(1) = 2$, $f(2) = 3$, $f(3) = 2$, $f(4) = 3$, $f(5) = 2$.

Since $f(1) = f(3) = f(5) = 2$, the function is not one-to-one.

Since $f(2) = f(4) = 3$, the function is not one-to-one.

Therefore, the function does not have an inverse.

3. Final Answer

No, this function does not have an inverse.