Answer:
The only zero of [tex]F^{-1}(x)[/tex] is [tex]3[/tex].
Step-by-step explanation:
The function [tex]F^{-1}[/tex] is the inverse of function [tex]F[/tex].
For a given [tex]x[/tex] and a given [tex]y[/tex], [tex]F^{-1}(y) = x[/tex] if and only if [tex]F(x) = y[/tex].
Let [tex]y[/tex] be a zero of [tex]F^{-1}(y)[/tex]. That is, [tex]F^{-1}(y) = 0[/tex].
By the reasoning above, since [tex]x = 0[/tex] and this particular [tex]y[/tex] satisfy [tex]F^{-1}(y) = x[/tex], it must be true that [tex]F(x) = y[/tex] for the same [tex]x = 0\![/tex] and [tex]y\![/tex].
Since [tex]x = 0[/tex] and [tex]F(x) = x + 3[/tex], [tex]F(0) = 3[/tex]. Therefore, [tex]y = F(0) = 3[/tex] since [tex]y = F(x)[/tex].
Thus, the zero of [tex]F^{-1}(y)[/tex] would be [tex]y = 3[/tex].
