Define a function y = P(x) that represents the "period" of g(x)=sin(f(x)) or h(x) = cos(f(x)) provided that f is a continuous non-linear function. (The period is the interval of x-values over which sin(f(x)) or cos(f(x)) varies through one full cycle of values).  Under what conditions is P(x) an increasing function? Under what conditions is P(x) decreasing? Define f so that P(x) is a non-constant linear function of x.

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