differential and invertable function f (x)

Question

1. The table below gives some value for a differential and invertable function f and it’s derivative f'

X	F(x)	F’(x)
0	49	0
1	2	-8
2	-1	-80

Use the above table to find the value of (f^-1)'(2). Hint: You can determine f^-1(2) using the information in the table.

Answer 1

The answer is -1/8

Dx[ f_inv(x)] = 1/ f' (f_inv(x)) by Theorem

Dx[ f_inv(2)] = 1/ f' (f_inv(2)) = 1/f'(1) = 1/-8