\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the function \(f\) defined on \(\mathbb{R}\) by:$$ f(x) = \begin{cases} 1-x & \text{if } x \ge 1 \\ (x-1)(x+1) & \text{if } x < 1 \end{cases} $$Prove that the function \(f\) is continuous on \(\mathbb{R}\).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.