Can you please provide a detailed solution for this Thanks i

Can you please provide a detailed solution for this? Thanks in advance!

Let f(x) = -x\' + 2x - 3. Find the value of d/dx f-1(x)|x = 1 at the point x = 1 = f(-2)

Solution

f\' =-3x^2 + 2

f(-2) =1 => f^-1 (1) = -2

d/dx [ f^-1 (x) ]

= 1/[ f\'(-2) ]

= 1/[ -3*(-2)^2 + 2]

=-0.1