Given:
The given absolute value function is,
[tex]f(x)=\lvert{x-5}\rvert[/tex]
Required:
To write the given absolute value function f as a piecewise function.
Explanation:
The given absolute value function can be written as:
[tex]\begin{gathered} f(x)=\begin{cases}{x-5,\text{ }x-5\ge0} \\ {-(x-5),\text{ }x-5\leq0} \\ {}\end{cases} \\ \Rightarrow f(x)=\begin{cases}{x-5,\text{ }x\ge5} \\ {-x+5,\text{ }x<5} \\ {}\end{cases} \end{gathered}[/tex]
Final Answer:
The given absolute value function f can be written as a piecewise function as follows:
[tex]f(x)=\begin{cases}{x-5,\text{ }x\ge5} \\ {-x+5,\text{ }x<5} \\ {}\end{cases}[/tex]
Option A is correct.
