The inverse function is f(x) = [tex] \frac{x + 4}{3} - 2 [/tex], which makes the inverse at x = 2 equal to 0.
All inverse functions can be found by switching the x and f(x) values. Once that is done, solve for the new f(x) value. The result will be the inverse of the original function. The step-by-step process is below.
f(x) = 3(x + 2) - 4 ----> Switch the x and f(x)
x = 3(f(x) + 2) - 4 ----> Add 4 to both sides
x + 4 = 3(f(x) + 2) ----> Divide both sides by 3
[tex] \frac{x + 4}{3} [/tex] = f(x) + 2 ----> Subtract 2 from both sides.
f(x) = [tex] \frac{x + 4}{3} - 2 [/tex]
The end is your inverse function. So then we can evaluate when x = 2.
f(x) = [tex] \frac{x + 4}{3} - 2 [/tex]
f(2) = [tex] \frac{2 + 4}{3} - 2 [/tex]
f(2) = [tex] \frac{6}{3} - 2 [/tex]
f(2) = [tex] 2 - 2 [/tex]
f(2) = 0
