# How can I find the domain of $x$ for which the function $g(x)\geq0\;$?

I have this function ($$x>0$$) $$f (x)=\frac{\sqrt{g (x)}+4 x \left(x^2+1\right) \sin (\pi x) \cos ((3+\pi ) x)}{x^4+2 x^2+1+\left(4 x^2+\left(x^2-1\right)^2 \cos (2 \pi x)\right)}$$

f[x_] := (   Sqrt[g[x]] + 4 x (1 + x^2) Cos[(3 + π) x] Sin[π x])/(   1 + 2 x^2 + x^4 + (4 x^2 + (-1 + x^2)^2 Cos[2 π x])); 

where $$g(x)=4 x^2+\left(x^2-1\right)^2 \cos (2 \pi x)-\left(x^2+1\right)^2 \cos (2 (3+\pi ) x)\;$$.

g[x_] := 4 x^2 + (-1 + x^2)^2 Cos[2 π x] - (1 + x^2)^2 Cos[      2 (3 + π) x]; 

I want to check the range of function $$f(x)$$ for those values of $$x$$ in which $$g(x)\geq0\;$$.

-How can I find the domain of $$x$$ for which $$g(x)\geq0\;$$?