Sketch the graphs of f(x) = arccos (cos(x)) and g(x)= cos(arccos(x)) on the separate axes below. Explain, in terms of the meaning of the input and output quantities of these functions, why your graphs look as they do. Your graphs should clearly indicate the domain and range of the functions f and g.

We have to sketch graphs of functions

f(x) =arccos(cos(x))

g(x) = cos(arccos(x)) 

arccos(x) means cos^-1x when x [-1, 1]

Thus, f(x) = cos^-1(cos(x)) 

and     g(x) = cos (cos^-1(x)) 

Domain of function = 

All values of x for which function gives a real value. 

Range of function = value of function corresponding to each element of domain.