Does there exists a transcendental entire function having no fixed points?

Question

Does there exists a transcendental entire function having no fixed points?

I think yes, there exist a transcendental entire function having no fixed point...

As I take $ f(z) = e^z + 1$

Is it true or false?

Answer 1

It should be $$ e^z + z $$ because $e^z + z = z$ implies...