Questions: f(x)= - if x <= 3, then -x^2 + 2x - 1 - if x > 7, then -x + 7 f(5)= Undefined

Solution Steps

To solve for \( f(5) \) given the piecewise function, we need to determine which part of the function applies to \( x = 5 \). The function is defined as: \[ f(x)=\left\{\begin{array}{ll} -x^{2}+2x-1 & \text{if } x \leq 3 \\ -x+7 & \text{if } x > 7 \end{array}\right. \] Since \( 5 \) does not satisfy either \( x \leq 3 \) or \( x > 7 \), the function is undefined at \( x = 5 \).

The given piecewise function is defined as follows: \[ f(x)=\left\{\begin{array}{ll} -x^{2}+2x-1 & \text{if } x \leq 3 \\ -x+7 & \text{if } x > 7 \end{array}\right. \]

To find \( f(5) \), we need to check which condition \( x = 5 \) satisfies:

• \( 5 \leq 3 \) (False)
• \( 5 > 7 \) (False)

Since \( 5 \) does not satisfy either condition, we conclude that the function is undefined at this value.

Since \( f(5) \) is not defined based on the conditions of the piecewise function, we can state that:

\[ f(5) = \text{Undefined} \]

Final Answer