So to find the inverse of this function, replace f(x) with y, switch x and y, then solve for y. This is what it'll look like: [tex] x=\frac{y-5}{3} [/tex]
Firstly, multiply both sides by 3: [tex] 3x=y-5 [/tex]
Next, add both sides by 5 and replace y with f^-1 (x) and your inverse equation is: [tex] 3x+5=f^{-1}(x) [/tex]
Now that we have the inverse, plug in 3 into it and solve:
[tex] 3(3)+5=f^{-1}(3)\\ 9+5=f^{-1}(3)\\ 14=f^{-1}(3) [/tex]
In short, the answer is 14, or the second option.
