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You should do :

sage: f.is_symmetric()
True

Now, the is_SymmetricFunction is too specific to be in the global namespace, its source code is :

return isinstance(x, SymmetricFunctionAlgebra_generic.Element)

You should do :do:

sage: f.is_symmetric()
True

Now, the The source code of is_SymmetricFunction is too specific to be in the global namespace, its source code is : function is:

return isinstance(x, SymmetricFunctionAlgebra_generic.Element)

sage: is_SymmetricFunction??

You should do:

sage: f.is_symmetric()
True

The Indeed, the source code of is_SymmetricFunction function is:

return isinstance(x, SymmetricFunctionAlgebra_generic.Element)

see:

sage: is_SymmetricFunction??

sage: f.parent()
Multivariate Polynomial Ring in x1, x2, x3 over Rational Field