A scalar function is defined as:
'A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.'
Therefore, if we have the following function
[tex]f(x)=y[/tex]
Given the x, y is unique.
The inverse function, takes the function value to its corresponding x value.
[tex]f^{-1}(f(x))=f^{-1}(y)=x[/tex]
In our problem, we have the following function values
[tex]\begin{gathered} g(5)=-3 \\ g(4)=1 \\ g(3)=-2 \\ g(2)=0 \end{gathered}[/tex]
If we apply the inverse function on all of those values, we should get the argument of the function back.
[tex]\begin{gathered} g^{-1}(g(5))=g^{-1}(-3)=5 \\ g^{-1}(g(4))=g^{-1}(1)=4 \\ g^{-1}(g(3))=g^{-1}(-2)=3 \\ g^{-1}(2)=g^{-1}(0)=2 \end{gathered}[/tex]
Therefore, from the possible answers, only (1, 4) belongs to the inverse.
