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

Question id: 633. This question is similar to one that appeared on an IB AA Higher paper in 2022. The use of a calculator is allowed.

Consider the function \(f(x) = \dfrac{x^3+2x}{5}, \; x \in \mathbb{R}\).

(a) Show that \(f\) is an odd function.

The function \(g\) is given by:

$$ g(x) = \dfrac{3x-3}{x^2+x-2} \quad \text{ where } x \in \mathbb{R}, x \neq 1, \; x \neq -2.$$ (b) Solve the inequality \( f(x) \lt g(x) \).
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