Exponential function/Secants/Intersection point/Exercise

Let

${}f(x)=a^{x}\,$

be an exponential function with ${}a\neq 1$. For every ${}x\in \mathbb {R}$, the line defined by the two points ${}(x,f(x))$ and ${}(x+1,f(x+1))$ has an intersection point with the ${}x$-axis, which we denote by ${}s(x)$. Show

${}s(x+1)=s(x)+1\,.$

Sketch the situation.

Create a solution