Question

In Exercises \(67 - 70\) , use the following function. \(f ( x ) = \left\\{ \begin{array} { l l } { 2 - x , } & { x \leq 1 } \\ { \frac { x } { 2 } + 1 , } & { x > 1 } \end{array} \right.\) Multiple Choice What is the value of \(f ( 1 ) ?\) (A) 5\(/ 2 \quad\) (B) 3\(/ 2 \quad\) (C) (D) 0 1(E) does not exist

Short answer

The value of \(f(1)\) is 1.

Step-by-step solution

Determine which part of the piecewise function to use

The first step is to see where the value \(x = 1\) falls in the given intervals of the piecewise function. There are two intervals in the function: \(x \leq 1\) and \(x > 1\). Since \(x = 1\) is not greater than 1, we have to use the first interval \(x \leq 1\) where the function is defined as \(2 - x\).

Substitute \(x = 1\) into the correct function interval

Now that we know that we need to use the first function interval for \(x \leq 1\), we can substitute \(x = 1\) into this part of the function. The expression \(\(2 - 1\) \) is used to find \(f(1)\).

Calculate \(f(1)\)

Substituting \(x = 1\) into the expression gives us \(2-1=1\). Therefore, \(f(1) = 1\).