# Problems from The absolute value function

Indicate the domain and the image of the following function: $$h(x)=|3x|$$

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### Development:

In this case the function is equivalent to: $$|3x|=\left\{\begin{array}{rcl} 3x & \mbox{ if } & 3x\geq0 \\ -3x & \mbox{ if } & 3x < 0 \end{array}\right.$$$And this is equivalent to: $$|x|=\left\{\begin{array}{rcl} 3x & \mbox{ if } & x\geq0 \\ -3x & \mbox{ if } & x < 0 \end{array}\right.$$$

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

### Solution:

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

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