On separate diagrams, sketch the graphs of \(y=f(|x|)\) and \(y=|f(x)|\), giving the coordinates of any points where the graphs meet the \(x\)- and \(y\)-axes. You should label the graphs clearly.[3]
State the set of values of \(x\) for which \(f(|x|)=|f(x)|\).[1]
Find the exact value of the constant \(a\) for which \(\displaystyle\int_{-1}^1 f(|x|)\,\mathrm dx=\int_1^a|f(x)|\,\mathrm dx\).[3]