Answer:Final answer is [tex]f(x)+g(x)=0.5x^2+8x^3[/tex]Step-by-step explanation:Given functions are [tex]f\left(x\right)=0.5x^2-2[/tex] and [tex]g(x)=8x^3+2[/tex]Now we need to add both functions:[tex]f(x)+g(x)[/tex][tex]=(0.5x^2-2)+(8x^3+2)[/tex][tex]=0.5x^2-2+8x^3+2[/tex][tex]=0.5x^2+8x^3-2+2[/tex]combine like terms -2 and +2[tex]=0.5x^2+8x^3[/tex]Hence final answer is [tex]f(x)+g(x)=0.5x^2+8x^3[/tex]