Rational Function

Algebra Level 4

Consider the function \(f(x)=\dfrac{x^{2}+ax+b}{x^{2}+2x+3}\) where \(a\) and \(b\) are positive integers.

If the range of \(f(x)\) is \([-5,4],\) find the value of \(a^{2}+b^{2}-ab.\)

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