Question

Erify that f has an inverse. then use the function f and the given real number a to find (f −1)'(a). (hint: see example 1. if an answer does not exist, enter dne.) f(x) = x + 2 x − 1 , x > 1 a = 2

Answer 1

The function

... f(x) = (x+2)/(x-1) = 1 + 3/(x-1)

is symmetrical about the line y=x, hence is its own inverse.

We can evaluate the desired derivative directly.

... f'(x) -3/(x-1)²

so f'(2) is

... f'(2) = -3/(2-1)²

$(f^{-1})(2)=-3$