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 don't see the original function in your message — could you paste it? Without it I can only give the general facts:

- If f is differentiable and invertible, the derivative (slope) of the inverse at a point y = f(x) is
(f^{-1})'(y) = 1 / f'(x) = 1 / f'(f^{-1}(y)).

- The x‑intercept of f^{-1} is the x value where f^{-1}(x)=0. That is the number X such that f(0)=X, so
x‑intercept of f^{-1} = f(0).

If your f is linear, f(x)=m x + b, then the inverse is f^{-1}(x) = (x − b)/m, so:
- slope of the inverse = 1/m,
- x‑intercept of the inverse = b.

Send the specific function and I’ll compute the required values.