# Prove that a set is decidable using time constructible function

I'm preparing an exam of theory of computation and I'm very in trouble with some exercise. Considering a Turing machine $$\mu$$ of alphabet $$A=\{ 0,1 \}$$ (we don't know nothing about termination) and a function $$f$$ that is time-constructible prove that : $$X=\{X \in A^* | \: \text{the computation of \mu associate to 'xx' does not terminate in f(|x|) steps} \}$$ is decidable. I have to establish also if $$X \in DTIME(f(n))$$ or in another class.
I know that a function $$f: \mathbb{N} \rightarrow \mathbb{N}$$ is known to be time-constructible if exist a Turing maching $$\mu$$ with $$k\in\mathbb{N}$$ tapes of alphabet $$A$$ such that $$\{0,1\} \subset A$$ e $$\forall \omega$$ input , the arrest time is $$T_\mu (\omega)=f(|\omega|).$$