## Exam-Style Question on Functions## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 676. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is allowed.

A function \( g \) is defined by \( g(x) = \frac{3x - 10}{x^2 - 9} \), where \( x \in \mathbb{R} \), \( x \neq \pm3 \).

(a) Determine the range of \( g \).

A function \( h \) is defined by \( h(x) = g(|x|)\sin(t) \), where \( x \in \mathbb{R} \), \( x \neq \pm3 \) and \( t \) is a constant where \( -\pi < t < 0 \).

(b) Find the set of values of \( x \) such that \( h(x) \geq 0 \).

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