Mt. Fuji, a mountain with mathematical beauty

This is Mt. Fuji, the highest mountain in Japan.
Mt. Fuji has well-proportioned cone shape, and is so famous that many Japanese children make or draw a mountain in the shape of Mt. Fuji when they are asked to "Create a mountain with clay" or "Draw a picture of a mountain." Therefore, when teachers first introduce a three-dimensional figure called the "cone," by simply saying "like Mt. Fuji," students easily visualize the figure.
Once a university in Japan arranged the following math problem for their entrance examination. Try solving this if you like. Only those students who have firmly climbed the long mountain paths of mathematics to the high school level would have had a wonderful view on their answer sheets.
Draw the graph of the following two curves on a coordinate plane.
f(x)= x^4-x^2+6 (|x|<=1), 12/(|x|+1) (|x|>1)
g(x)= 1/2*cos(2πx)+7/2 (|x|<=2)
Source: Shizuoka University, 2000