let be a function given by $ f^{-1} (x) = \sqrt x + G(x) $
with $ G(x)= \sum_{n=0}^{N}a_{n} \sin(nx+ \pi/4) $ finite fourier series with N big
my questio is , if for $ x \rightarrow \infty$ the function can be asymptotically defined by $ f(x) \sim x^{2} $
on condition that for every 'x' $ G(x) \le \le \sqrt x$ so the most importan term is the SMOOTH term defined by the square root of 'x'