Chapter 3

Suppose that \(f(x)\) and \(g(x)\) are effectively computable functions. Prove, using Church's thesis, that the function \(h\) given by \(h(x)= \begin{cases}x & \text { if } x \in \text { Dom }(f) \cap \operatorname{Dom}(g), \\ \text { undefined } & \text { otherwise }\end{cases}\) is URM-computable.

Devise Turing machines that will Turing-compute the functions (a) \(x-1\) (b) \(2 x\).