Question

if f(x)=√x-x and g(x)=2x^3-√x-x find f(x)-g(x)

Answer 1

Given:

$\begin{gathered} f(x)=\sqrt{x}-x \\ g(x)=2x^3-\sqrt{x}-x \end{gathered}$

Required:

Find f(x) - g(x).

Explanation:

The given functions are:

$\begin{gathered} f\mleft(x\mright)=√x-x \\ g\mleft(x\mright)=2x^3-√x-x \end{gathered}$$\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}$

Final Answer:

$f(x)-g(x)=2(\sqrt{x}-x^3)$