Explanation
So we are given two functions f(x) and g(x) and we must find the expression for f(x)-g(x). We just need to take the expression for f(x) and substract that of g(x) from it:
[tex]\begin{gathered} f(x)-g(x)=\sqrt{x}-x-(2x^3-\sqrt{x}-x) \\ f(x)-g(x)=\sqrt{x}-x-2x^3+\sqrt{x}+x \end{gathered}[/tex]
Then we group like terms and we add/substract them:
[tex]\begin{gathered} f(x)-g(x)=\sqrt{x}-x-2x^3+\sqrt{x}+x=-2x^3+\sqrt{x}+\sqrt{x}+x-x \\ f(x)-g(x)=-2x^3+(1+1)\sqrt{x}+(1-1)x \\ f(x)-g(x)=-2x^3+2\sqrt{x} \end{gathered}[/tex]Answer
Then the answer is option D.
