Question

How can function f be written as a piecewise function?

Answer 1

Given:

The given absolute value function is,

`f(x)=\lvert{x-5}\rvert`

Required:

To write the given absolute value function f as a piecewise function.

Step-by-step explanation:

The given absolute value function can be written as:

`\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}`

Final Answer:

The given absolute value function f can be written as a piecewise function as follows:

`f(x)=\begin{cases}{x-5,\text{ }x\ge5} \\ {-x+5,\text{ }x<5} \\ {}\end{cases}`

Option A is correct.