Question

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

Explanation:

Step1: Recall inverse function point property

If $(a,b)$ is on $f^{-1}(x)$, then $(b,a)$ is on $f(x)$.

Step2: Apply property to given point

Given point $(-1, 0.5)$ on $f^{-1}(x)$, swap coordinates: $(0.5, -1)$.

Answer:

(0.5, -1)