Question: How to do these function compositions?

f(x, g(x,y)) + f(g(x,y), y) >= f(g(x,y), g(x,y))
f(x, g(x,y)) + f(x, g(x,y)) >= f(g(x,y), y)

f(x, g(x,y)) + f(x, g(x,y)) >= g(f(x,y), y)

f(x, g(x,y))*f(x, g(x,y)) >= f(g(x,y), y)

how to create a combinations of function of another function in maple

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