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Suppose $f(x)$ is a function that has this property: For all real numbers $a$ and $b$ such that \(a , the portion of the graph of $y=f(x)$ between $x=a$ and $x=b$ lies below the line segment whose endpoints are $(a,f(a))$ and $(b,f(b))$. (A function with this property is called strictly~convex.) Given that $f(x)$ passes through $(-2,5)$ and $(2,9)$, what is the range of all possible values for $f(1)$? Express your answer in interval notation.