Theory of computation, computer science, Basic Computer Science

I define a restricted form of TMs M as follows. Given any input x on the tape of M, the initial portion of the tape that holds x is read-only and one-way. That is, M cannot write on input x, and M cannot move back (to the left) on input x. But beyond this portion of x, M works as a normal TM. What kind of languages can be accepted by this restricted form of TMs? Is the emptiness (i.e., whether a given TM in the restricted form accepts a non-empty language) is decidable? Prove it.
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