Given:
The graph of an invertible function [tex]f[/tex] is given.
To find:
The value of [tex]f^{-1}(-3)[/tex].
Solution:
We know that, if the graph of an invertible function [tex]f[/tex] passes through the point (a,b), then the inverse function [tex]f^{-1}[/tex] passes through the point (b,a).
From the given graph it is clear that the graph of the function [tex]f[/tex] passes through the points [tex](-5,-3)[/tex].
So, the inverse function [tex]f^{-1}[/tex] must be passes through the point [tex](-3,-5)[/tex].
Therefore, the value of inverse function is [tex]-5[/tex] at [tex]x=-3[/tex]. So, the value of [tex]f^{-1}(-3)[/tex] is [tex]-5[/tex].
