products of function equivalence classes

The1TL

1. The problem statement, all variables and given/known data

If f ∈ C(R) with f(0) ≠ 0, show that there exisits a g ∈ C(R) such that [fg] = [1], where [1] denotes the equivalence class containing the constant function 1.

2. Relevant equations



3. The attempt at a solution
Let f ∈ C(R) such that f:R → R is defined as f(x) = 1/x and let g ∈ C(R) such that g:R → R is defined as g(x) = x. Therefore [fg] = [x/x] = [1] for all x∈R.

is this correct?

HallsofIvy

"The equivalence class containing the constant function 1" with what equivalence relation?