what are the domain and range of $f(x)=2|x - 4|$?\no domain: $xleq2$; range: $(-infty,infty)$\no domain…

Explanation:

Step1: Determine the domain

The function $f(x)=2|x - 4|$ is an absolute - value function. There are no restrictions on the value of $x$ for which the function is undefined. So, the domain is all real numbers, which can be written as $(-\infty,\infty)$.

Step2: Determine the range

The absolute - value function $|x - 4|$ has a non - negative output for all real $x$, i.e., $|x - 4|\geq0$ for all $x\in(-\infty,\infty)$. Then $f(x)=2|x - 4|\geq0$ since we are multiplying the non - negative value of $|x - 4|$ by a positive number 2. So the range of the function is $f(x)\geq0$.

Answer:

domain: $(-\infty,\infty)$; range: $f(x)\geq0$