What are trivial functions.

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In a book on probability theory there was a statement that:

"Probability function P[x] is a non trivial function of x."

I don't know the meaning of "non-trivial" functions?

I tried searching on net but there were many problems discussing about non trivial function but nowhere its exact definition was given.

I found this desmos link, here I thought that g(x) is a non trivial function of x. But g(x) can be written as g(x)=f(8x)=8x-1. Then whats so special about g(x) here.

Kindly help me with the definition of trivial/non-trivial function. And how P[x] is a non-trivial function of x?