Question

If $f\left(x\right)=|2x^3+x-7|,$ then

• A. $f\left(x\right)=2x^3+x-7$ when $2x^3+x-7\ge 0$
• B. $f\left(x\right)=2x^3+x-7$ when $2x^3+x-7\le 0$
• C. $f\left(x\right)=7-2x^3-x$ when $2x^3+x-7<0$
• D. $f\left(x\right)=7-2x^3-x$ when $2x^3+x-7>0$

Answer 1

Answer: (A), (C)

The correct options are
A $f\left(x\right)=2x^3+x-7$ when $2x^3+x-7\ge 0$
C $f\left(x\right)=7-2x^3-x$ when $2x^3+x-7<0$

$f\left(x\right)=\{\begin{array}{cc}2x^3+x-7,& 2x^3+x-7\ge 0\\ -(2x^3+x-7),& 2x^3+x-7<0\end{array}$
$\Rightarrow f\left(x\right)=\{\begin{array}{cc}2x^3+x-7,& 2x^3+x-7\ge 0\\ 7-2x^3-x,& 2x^3+x-7<0\end{array}$