Period, range and a shifted cosine form of a combined sinusoid, then an inequality with a quadratic

Let \(f(x)=5\sin\left(\frac{\pi x}{2}\right)-12\cos\left(\frac{\pi x}{2}\right)+20\) for \(x\in\mathbb{R}\).

1. Find the period and the range of \(f\).[3]
2. Express \(f(x)\) in the form \(a\cos\left(b(x-d)\right)+c\), where \(a\), \(b\), \(c\) and \(d\) are positive constants and \(0<d<4\).[4]
3. Solve the inequality \(f(x)\ge x^2\).[2]