For the function y = f ( x ) = x ^2 − 2 x − 3 , x ≥ 1 , find d f ^− 1 /d y ∣ ∣ ∣ y = − 2

Question

(f^-1)'(-2)=???

I do not know where to start!!

Answer 1

Let find for what x f(x) = - 2, x² - 2x - 3 = - 2, x² - 2x - 1 = 0, x = 1 + √2 or 1 - √2. Because x ≥ 1 we have to take x = 1 + √2.

Now d/dy(f^-1(-2)) = 1/f'(1 + √2) = 1/(2(1 + √2) - 2) = 1/(2√2) = √2/4