# Polynomial-time Computable $f \circ g$. What does this implies for $f$ and $g$

Suppose that $$f$$ and $$g$$ are functions and $$f \circ g$$ is polynomial computable.

a) is it true that $$f$$ is also polynomial computable

b) is it true that $$g$$ is also polynomial computable

c) if we replace "polynomial" by "logarithmic" would the previous questions be true?

What if $$f = 0$$?
What if $$g = 0$$ and $$f(0) = 0$$?