Inverse funksjonar

Eit nytt blikk på sprettballen

Hans Georg Schaathun

August 2016

$$h(t) = 10 - 4{,}9t^2$$

$$h^{-1}(y)$$

$$h(t) = 10 - 4{,}9t^2 = y$$

$$h(t) = 10 - 4{,}9t^2 \quad\quad\quad h^{-1}(y) = \sqrt{\frac{10-y}{4{,}9}}$$

$$h^{-1}(h(t)) = \sqrt{\frac{10-(10-4{,}9t^2)}{4{,}9}} = t$$

$$h(h^{-1}(y)) = 10 - 4{,}9\sqrt{\frac{10-y}{4{,}9}}^2 = y$$