Question

Consider the function and its inverse:






The slope, a, of the inverse function is
, and the x-intercept of the inverse function is at x =
.

Answer 1

I’m missing the original function (or its graph) — could you post that? With it I can compute the numerical answers.

Meanwhile, here are the general facts you’ll need:

- If f is differentiable and f(c) = d, then the derivative (slope) of the inverse at x = d is
(f^{-1})'(d) = 1 / f'(c).
So the slope a of the inverse at the point corresponding to c is a = 1 / f'(c).

- The x‑intercept of f^{-1} is where f^{-1}(x) = 0. That happens exactly when x = f(0). So the x‑intercept of the inverse is at x = f(0) (the point (f(0), 0)).

If you give the specific function (or the point where you want the inverse slope), I’ll compute the numeric values.