I have some problems to understand computability and hope you can help me. In the lecture we had following problem:
Consider the three partial functions $f,g,h\colon N \to N$, where $f$ is computable and $g$ is not computable. The following two statements are correct:
If $h(x) = g(f(x))$, then $h$ could be computable.
If $g(x) = h(f(x))$, then $h$ is not computable.
Well, 2 is clear I think, because we know that $g$ is not computable and $f$ is computable, so $h$ has to be not computable, otherwise $g$ would be computable.
But 1 is a big problem for me. If $f$ is computable and $g$ is not computable, how can $h$ be computable?