Given:
[tex]\begin{gathered} f(x)=\sqrt{x}-x \\ g(x)=2x^3-\sqrt{x}-x \end{gathered}[/tex]Required:
Find f(x) - g(x).
Explanation:
The given functions are:
[tex]\begin{gathered} f\mleft(x\mright)=√x-x \\ g\mleft(x\mright)=2x^3-√x-x \end{gathered}[/tex][tex]\begin{gathered} f(x)-g(x)=(\sqrt{x}-x)-(2x^3-\sqrt{x}-x) \\ =\sqrt{x}-x-2x^3+\sqrt{x}+x \\ =2\sqrt{x}-2x^3 \\ =2(\sqrt{x}-x^3) \end{gathered}[/tex]Final Answer:
[tex]f(x)-g(x)=2(\sqrt{x}-x^3)[/tex]