Indicate the domain and the image of the following function: $$h(x)=|3x|$$
See development and solution
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:
$$Dom (f) =\mathbb{R}$$, $$Im (f) = [0, +\infty)$$