the point (-1, 0.5) lies on the graph of $f^{-1}(x)=2^{x}$. based on this information, which point lies on…

Explanation:

Step1: Recall inverse - function property

If the point $(a,b)$ lies on the graph of $y = f^{-1}(x)$, then the point $(b,a)$ lies on the graph of $y = f(x)$.

Step2: Identify the given point on inverse - function

We are given that the point $(-1,0.5)$ lies on the graph of $f^{-1}(x)=2^{x}$.

Step3: Find the corresponding point on the original function

By the inverse - function property, if $a=-1$ and $b = 0.5$ for $y = f^{-1}(x)$, then for $y = f(x)=\log_{2}x$, the point is $(0.5,-1)$.

Answer:

$(0.5,-1)$