Answer :
The value of [tex]f^{-1}(6)[/tex] is [tex]-3[/tex].
Given:
The function [tex]f[/tex] has an inverse and [tex]f(-3)=6[/tex].
To find:
The value of [tex]f^{-1}(6)[/tex].
Explanation:
If a point [tex](a,b)[/tex] lies on the function [tex]f(x)[/tex], then the point [tex](b,a)[/tex] must lies on the inverse function [tex]f^{-1}(x)[/tex].
According to the given value [tex]f(-3)=6[/tex], the point [tex](-3,6)[/tex] lies on the function [tex]f(x)[/tex]. So, the point [tex](6,-3)[/tex] must be lies on [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(6)=-3[/tex]
Therefore, the value of [tex]f^{-1}(6)[/tex] is [tex]-3[/tex].
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