Question

How do you prove that f(x)= x is the identity function?

Answer 1

By definition? The left and right sides of the equation are always identical for all x.

Answer 2

Or substitution: if f(x) = x, replace f(x) with x, and the equation becomes x=x.

Answer 3

ok then in trems of g circle f = g circle f is true if f(x)=x is the identity

Answer 4

'g circle f' is read as "g of f" (composition of function g with function f, g o f = g(f(x) ).
If f(x)=x, then g(f(x)) = g(x).