The inverse function is equal to f-1(x) = (x - 1)/3 and the value at f-1(6) is equal to 5/3.
To find the inverse, you need to switch the f(x) and x in the equation. Then you can solve for the new f(x). The result will be the inverse (f-1)
f(x) = 3x + 1 ----> Switch f(x) and x
x = 3f(x) + 1 ----> Subtract 1
x - 1 = 3f(x) ----> Divide by 3.
f-1(x) = (x - 1)/3
Now that we have the inverse, we can plug 6 in to get the value at f-1(6).
f-1(x) = (x - 1)/3
f-1(6) = (6 - 1)/3
f-1(6) = 5/3