I am attempting to find the derivative of an inverse at a point 'a'. In this case it is not suitable to find the inverse of the function by hand.

I understand we use the derivative of an inverse formula,

d/dx[(f^-1)'(a)] = 1/f'(b)

We can use the properties of an inverse function to evaluate this. Consider that our input 'a' into our inverse function will produce output 'b', where output 'b' into our original function will produce output 'a'.

aka (x,y) values for inverse and original functions are swapped.

Therefore f(b) = a

We are given 'a' as 1

Therefore solve for f(b) = 1

But, we cannot solve for f(b) = 1 as f(x) is some function unable to managed by hand.

The solution can be find graphically of course but this question requires you to find it by hand.

I am stumped on how you can approach this, all the examples I see online feature instances where you can easily find f(b) = a.