Maths Paper 1, November 2024, question 5.4

The graph of $f(x)={\displaystyle \frac{-6}{x-2}}-2$ is drawn in the diagram below. Its domain is $x\in (-\mathrm{\infty };2)\cup (2;\mathrm{\infty })$. The graph cuts the $y$-axis at $(0;1)$ and the line $g(x)=x-4$ is a line of symmetry of $f$. Determine the values of $x$ for which $f(x)\ge 0$.