Suppose \(f(x)\) is a function that has this property: For all real numbers a and b such that a \(y=f(x)\) 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.
