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Exam-Style Question on Functions

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Question id: 705. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is not allowed.

The function \( f \) is defined by \( f(x) = \frac{5x + 5}{3x - 6} \) for \( x \in \mathbb{R}, x \neq 2 \).

(a) Find the zero of \( f(x) \).

(b)For the graph of \( y = f(x) \), write down the equation of the asymptotes;

(c) Find \( f^{-1}(x) \), the inverse function of \( f(x) \).

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