B

In the picture A, the graph of the quadratic function \( f(x) = x^2\) is shown. With the aid of the graph of \(f\) identify which of the graphs shown in the picture B is the graph of \( g(x) = -\frac{1}{2} x^2\). What is the color of the graph of \(g\)? (Note: Each graph in the picture B is the graph of some transformation of \(f\).)

Assuming \(x\in \mathbb{R}\), find the solution set of the following equation. \[ (x^3-1)x^2=0 \]

Use the picture to find the solution set of the inequality. \[ x^4 < x^2 \]

Find the solution set of the inequality. \[ (x^2-1)(x^2+1)>0 \]