### Instruction: Suppose the point $(1,2)$ is on the graph of $y=\frac{f(x)}2$. Then there is one point which must be on the graph of $y=\frac{f^{-1}(x)}{2}$. What is the sum of that point's coordinates?### Response: Let's substitute $x=1$ into $y=\frac{f(x)}2$ to find out what $f(1)$ is.
That gives $f(1)=4$.
Now we need to find the point on the graph of $y=\frac{f^{-1}(x)}{2}$ that has $x=4$.
Right. So we substitute $x=4$ into $y=\frac{f^{-1}(x)}{2}$ to get $y=\frac{f^{-1}(4)}{2}$.
So we need to find $f^{-1}(4)$.
We know that $f(1)=4$, so $f^{-1}(4)=1$.
That means $y=\frac{1}2$.
So the point must be $(4,\frac{1}2)$.