Question

evaluate the piece - wise function when (x = 4) and (x = 7).(f(x)=\begin{cases}-\frac{1}{4}x - 7, &\text{if }xleq4\\x - 3, &\text{if }x>4end{cases})the value of (f) is when (x = 4).the value of (f) is when (x = 7).

Explanation:

Step1: Evaluate for x = 4

Since \(x = 4\) and the condition for the first - part of the piece - wise function is \(x\leq4\), we use \(f(x)=-\frac{1}{4}x - 7\). Substitute \(x = 4\) into the formula: \(f(4)=-\frac{1}{4}\times4-7\).
\[

$$\begin{align*} f(4)&=- 1-7\\ &=-8 \end{align*}$$

\]

Step2: Evaluate for x = 7

Since \(x = 7\) and the condition for the second - part of the piece - wise function is \(x>4\), we use \(f(x)=x - 3\). Substitute \(x = 7\) into the formula: \(f(7)=7 - 3\).
\[f(7)=4\]

Answer:

When \(x = 4\), the value of \(f\) is \(-8\).
When \(x = 7\), the value of \(f\) is \(4\).