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no, because xx=x squared, and x squared is not linear
No, f(x) = x + x^5 in not linear.
Only if it's a function.
The result depends on how the function f() is defined. Simply copy the function definition, replacing every "x" (assuming the function is defined in terms of "x") by "x+5".
If it were written in a book of some sort, fx or f(x) is read aloud as "f or x". "f" is a function of some variable, "x". By function it means something happens to x e.g. x2 or 3x+4.