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