Rational Connection!

Algebra Level 4

\[\large f(x)=\frac{ax^2+6x+b}{x^2-1} \:\:\text{and} \:\:\large g(x)=\frac{(a+b)x^2+60x-54}{x^2-1}\]

Let \(f(x)\) and \(g(x)\) be defined by the given formulas on the set \( \mathbb{R}-\{-1, 1\}.\) If the range of \(f(x)\) is the set \(\mathbb{R}\), then which one of the following is the range of \(g(x).\)

Inspiration

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