Problems from The absolute value function

Development:

In this case the function is equivalent to: $$|3x|=\{\begin{array}{rcl}3x& \text{ if }& 3x\ge 0\\ -3x& \text{ if }& 3x<0\end{array}$$ And this is equivalent to: $$|x|=\{\begin{array}{rcl}3x& \text{ if }& x\ge 0\\ -3x& \text{ if }& x<0\end{array}$$

Therefore $Dom(f)=\mathbb{R}$ and $Im(f)=[0,+\mathrm{\infty })$.

Solution:

$Dom(f)=\mathbb{R}$, $Im(f)=[0,+\mathrm{\infty })$

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