Question

given fg:(x)=4(x)²+4(x)-1,f(x)=2(x)+1
search g(x)

Answer 1

If by fg(x) you mean (fg)(x) = f(x) * g(x) then
g(x) = (4x^2+4x-1)/(2x+1) = 2x+1 - 2/(2x+1)
That doesn't seem likley. So if you meant
fg(x) = (f◦g)(x) = f(g(x)) then since
4x^2 + 4x-1 = 2(2x^2+2x-1) + 1
g(x) = 2x^2+2x-1