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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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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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why can we define P(x)= (2pi) / |f'(x)|? What steps?

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