Question 1031448
It is a fact that {{{-1 <= cos3x <= 1}}} for all real values x.

==> {{{1 >= -cos3x >= -1}}}
==> {{{3 >= 2-cos3x >= 1}}}, after adding 2 to all sides..
==> {{{1/3 <= 1/(2-cos3x) <= 1}}}, after inversion (notice that all terms are positive)

==> The range of f(x) is the closed interval [1/3, 1].