Given the functions \(f(x) = \frac{1}{4}{x^2}\) and \(h(x) = x\) then \(g(x) = f(x) + h(x)\) is?

Given the functions \(f(x) = {x^3}\) and \(h(x) = - 2{x^2}\) then \(g(x) = f(x) + h(x)\) is?

Given the functions \(f(x) = \frac{1}{8}{x^4}\) and \(h(x) = - {x^2}\) then \(g(x) = f(x) + h(x)\) is? 

Use the graphs of \(f(x) = - {x^2}\) and \(g(x) = |x|\) to sketch the graph of \(y = - {x^2} + |x|\).

Use the graphs of \(f(x) = \frac{1}{x}\) and \(g(x) = x\) to sketch the graph of \(y = \frac{1}{x} + x\).

i) On the same axes, sketch the curves \(y = \cos x,\, y = -\cos\dfrac{x}{2},\,\text{ and } y = \cos x - \cos\dfrac{x}{2}\), for \(-\pi \leq x \leq \pi\).

ii) From your graph, determine the number of values of \(x\) in the interval \(-\pi \leq x \leq\pi\) for which \(\cos x - \cos \dfrac{x}{2} = -1\).

iii) For what values of the constant \(K\) does \(\cos x - \cos\dfrac{x}{2} = K\) have exactly two solutions in the interval \(-\pi \leq x \leq \pi\)?