The value of the inverse at f-1(3) is [tex] \frac{4}{3} [/tex].
To find this, we first need to find the inverse function. We can do so by switching the f(x) and x value. Then we need to solve for the new f(x). The result will be the inverse function. The work for this function is below.
f(x) = 3x - 1 ----> Switch the x and f(x)
x = 3f(x) - 1 ----> Add 1 to both sides
x + 1 = 3f(x) ----> Divide both sides by 3.
f(x) = [tex] \frac{x + 1}{3} [/tex]
Now that we have the inverse function, we can evaluate it at x = 3
f(x) = [tex] \frac{x + 1}{3} [/tex]
f(3) = [tex] \frac{3 + 1}{3} [/tex]
f(3) = [tex] \frac{4}{3} [/tex]
