Given the function f(x) = 4(x+3) − 5, solve for the inverse function when x = 3.

The inverse function gives us -1 when x = 3.
In order to find this, we have to solve for the inverse. We do this by switching the x and f(x) values and then you can solve for the new f(x) value. The work for this is done below. 
f(x) = 4(x + 3) - 5 ----> Switch the x and f(x)x = 4(f(x) + 3) - 5-----> Add 5 to both sides. x + 5 = 4(f(x) + 3) ----> Divide both sides by 4. [tex] \frac{x+5}{4} [/tex] = f(x) + 3 ---> Subtract 3 from both sides. 
[tex] \frac{x+5}{4} [/tex] - 3 = f(x) 

Now that you've returned to f(x), you have the inverse. Now we can take the inverse equation and plug in for x = 3. 
f(x) = [tex] \frac{x+5}{4} [/tex] - 3 f(3) = [tex] \frac{3+5}{4} [/tex] - 3 f(3) = [tex] \frac{8}{4} [/tex] - 3 f(3) = 2-3f(3) = -1