Let $f(x)=2x-x^{2}$, find the range $r(f(x))$ of the function $f(x)$ I need to check whether my solutions are correct for the following problems:


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*$1)$ Let $f(x)=2x-x^{2}$, find $r(f(x))$.


My solution: $r(f(x))=(-\infty,1]$


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*$2)$ Let $f(x)=x^{2}-7x+10$. Find $f\left((0,6]\right)$ and $f^{-1}((4,10])$.


My solution: $f((0,6])=[-2.25,10)$ and $ f^{-1}((4,10])=[0,7]$
I solved these 2 by looking at their graphs.

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*Hint 
$$
f(f(x))=2 f(x)-(f(x))^2
$$

