Answer:
[tex]\large\boxed{(f+g)(x)=-3x^2+2x+1}[/tex]
Step-by-step explanation:
[tex]f(x+y)=f(x)+g(x)\\\\f(x)=-5x^2-3x+2,\ g(x)=2x^2+5x-1\\\\\text{Substitute:}\\\\(f+g)(x)=(-5x^2-3x+2)+(2x^2+5x-1)\\\\=-5x^2-3x+2+2x^2+5x-1\qquad\text{combine like terms}\\\\=(-5x^2+2x^2)+(-3x+5x)+(2-1)\\\\=-3x^2+2x+1[/tex]
