SOLUTION: Please help me with this calculus problem involving derivatives of inverse functions. Thank you in advance for your time! <a rel=nofollow HREF="https://ibb.co/L0fMQpv"><img src

One approach is to find g(x), the inverse of f(x):



f(x) = ,   



To avoid confusion, I'll use y=f(x), solve for y, and after that, we can write g(x):



  f(x) = 

Square both sides

  

Add 16 to both sides, this completes the square on RHS

  

Factor RHS

   

Take square root of both sides

  

Subtract 4 from both sides, and re-write with x on LHS:

  





Now we can write   , and g(x) also has domain 





g'(x) =  





Just plug in x=3 to g(x) and g'(x) to get the desired values ( I got g(3)=1, g'(3)=1/10)