Inverse functions are reflections across y = x
This animation plots e^x and ln x on the same coordinate grid alongside the line y = x, showing how the two curves mirror each other across that diagonal. A point at (1, e) visibly reflects to (e, 1), demonstrating how coordinates swap between a function and its inverse. The visual builds toward the identity f(f^{-1}(x)) = x, making an abstract algebraic rule concrete. Useful for precalculus or calculus students learning why exponential and logarithmic functions are inverses.
16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Apply ALL of the following review notes precisely; keep everything else identical. This video is for social media and must be impeccable. - Just missing a bit more flow and slightly better pacing, otherwise video is great
Make the next one in this series
- Show the same reflection idea using x^2 and sqrt(x) restricted to x >= 0
- Animate how the derivative of ln x follows from the derivative of e^x via inverse function rules
- Create a visual proof that any function reflected over y = x swaps its domain and range
