Question

If $f\left(x\right)=|8-4x|,$ then

• A. $f\left(x\right)=8-4x$ when $x\ge 2$
• B. $f\left(x\right)=8-4x$ when $x\le 2$
• C. $f\left(x\right)=4x-8$ when $x>2$
• D. $f\left(x\right)=4x-8$ when $x<2$

Answer 1

Answer: (B), (C)

The correct options are
B $f\left(x\right)=8-4x$ when $x\le 2$
C $f\left(x\right)=4x-8$ when $x>2$

$f\left(x\right)=\{\begin{array}{cc}8-4x,& 8-4x\ge 0\\ -(8-4x),& 8-4x<0\end{array}$
$\Rightarrow f\left(x\right)=\{\begin{array}{cc}8-4x,& 8\ge 4x\\ 4x-8,& 8<4x\end{array}$
$\Rightarrow f\left(x\right)=\{\begin{array}{cc}8-4x,& x\le 2\\ 4x-8,& x>2\end{array}$