Answer:
3
Step-by-step explanation:
Use the property:
[tex]f^{-1}(f(x))=x[/tex]
This implies that;
[tex]f^{-1}(f(3))=3[/tex]
The correct choice is the first option.
Or see it in details below:
Given
[tex]f(x)=9x+1[/tex]
substitute x=3, to obtain;
[tex]f(3)=9(3)+1=28[/tex]
Let [tex]y=9x+1[/tex]
Interchange x and y.
[tex]x=9y+1[/tex]
Solve for y.
[tex]x-1=9y[/tex]
[tex]\frac{x-1}{9}=y[/tex]
This implies that;
[tex]f^{-1}(x)=\frac{x-1}{9}[/tex]
[tex]f^{-1}(f(3))=f^{-1}(28)[/tex]
[tex]f^{-1}(28)=\frac{28-1}{9}[/tex]
[tex]f^{-1}(28)=\frac{27}{9}=3[/tex]
