Answer:
[tex]\large\boxed{(f+g)(x)=4x^2+\dfrac{3}{2}x-7}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=\dfrac{x}{2}-3=\dfrac{1}{2}x-3,\ g(x)=4x^2+x-4\\\\\text{Substitute:}\\\\(f+g)(x)=\left(\dfrac{1}{2}x-3\right)+(4x^2+x-4)\\\\=\dfrac{1}{2}x-3+4x^2+x-4\qquad\text{combine like terms}\\\\=4x^2+\left(\dfrac{1}{2}x+x\right)+(-3-4)\\\\=4x^2+1\dfrac{1}{2}x-7\\\\=4x^2+\dfrac{3}{2}x-7[/tex]
