+0  
 
0
17
1
avatar+12 

\(The function $f(x)$ is defined for $1 \le x \le 5$ as follows: \[f(x) = \left\{ \begin{array}{cl} -2x + 4 & \text{if }1 \le x \le 2, \\ 5 - x & \text{if }2 < x \le 3, \\ 9 - 2x & \text{if }3 < x \le 4, \\ 6 - x & \text{if }4 < x \le 5. \end{array}\right.\]Find all real numbers ${}x$ such that $f(x) = x$. \)
 

 Oct 22, 2023
 #1
avatar+624 
-1

To find the values of x such that f(x)=x, we need to solve each of the following equations:

2x+1=x

7−x=x

10−2x=x

10−x=x

Solving the first equation, we get x=−1​.

Solving the second equation, we get x=3.5​.

Solving the third equation, we get x=5​.

Solving the fourth equation, we get x=5​.

Therefore, the values of x such that f(x)=x are −1, 3.5, and 5.

 Oct 27, 2023

2 Online Users

avatar