The answer is: " 14 " .
_____________________________________________________
Step-by-step explanation:
_____________________________________________________
If f(x) = (x - 5) / 3 ;
_____________________________________________________
To get f⁻¹(x) ;
Take: " f(x) = (x - 5) / 3 ;
Substitute "y" in lieu of the notation, " f(x)" ;
and write as: "y = (x - 5) / 3 " ;
Then, replace "x" with "y"; and "y" with x" ;
______________________________________
"x = (y -5) / 3 " ;
______________________________________
Now, rewrite, solving for "y" in terms of "x" ;
______________________________________
y - 5 = 3x ;
Add "5" to each side of the equation; to isolate "y" on one side of the equation, and to solve for "y" in terms of "x" ; y - 5 + 5 = 3x + 5 ;
y = 3x + 5 ;
Now, substitute: "f⁻¹(x)" for "y" ; and rewrite:
f⁻¹(x) = 3x + 5 .
_________________________________________
The question asks: " Solve f⁻¹(3) ".
We have: " f⁻¹(x) = 3x + 5 " ; so; to find, " f⁻¹(3)" ; we plug in "3" for the values of "x" in the expression and solve;
f⁻¹(3) = 3(3) + 5 = 9 + 5 = 14.
_____________________________________________
The answer is: " 14 " .
_____________________________________________