Can I replace the 'if' inside of the epsilon-delta definition of a limit with an 'if and only if'

Question

You can write x as a function of f(x) or equivalently find the inverse function which 'switches' the axes around which causes the new definition of a limit to switch the epsilon and delta along with the 'x' and 'f(x)'.

Here is the epsilon-delta definition of a limit for reference. 0<∣x−x 0 ​ ∣<δ ⟹ ∣f(x)−L∣<ε.

Answer 1

No, it's not an "if and only if". For a continuous function, that would require $$|f(x_0 - \delta) - f(x_0)| = |f(x_0+\delta) - f(x_0)| = \varepsilon$$