Answer
False
Work Step by Step
If we must take a square root to solve for $y=f(x)$, by convention, only the positive square-root value is kept, resulting in $y=f(x)$ to only encompass half of the graph and leave out the negative part of the graph. Thus, it is not necessarily true that the graph of the equation and the graph of $f$ are the same.
For example, the implicit equation for a circle is $x^2 + y^2 = 1$. Yet, solving for $y$ only results in the positive solution by convention: $y = \sqrt{1-x^2}$.
