Find f(8) for this piecewise-defined function.
f(x)=
4x–5	if x≤1
1
6
x–1	if x>1
Write your answer as an integer or as a fraction in simplest form.
f(8)=

To find \( f(8) \), we need to identify which part of the piecewise function to use based on the value of \( x = 8 \).

The function is defined as:

\[
f(x) = \begin{cases} 
4x - 5 & \text{if } x \leq 1 \\
\frac{1}{6}(x - 1) & \text{if } x > 1 
\end{cases}
\]

Since \( 8 > 1 \), we will use the second part of the function:

\[
f(x) = \frac{1}{6}(x - 1)
\]

Substitute \( x = 8 \) into the expression:

\[
f(8) = \frac{1}{6}(8 - 1) = \frac{1}{6}(7) = \frac{7}{6}
\]

So, \( f(8) = \frac{7}{6} \).

### Answer:
\[
f(8) = \frac{7}{6}
\]

Do you want more details or have any questions?

Here are five related questions:
1. How do you simplify a fraction to its simplest form?
2. What is a piecewise function and how does it work?
3. How would you calculate \( f(x) \) for \( x = 0 \) in this function?
4. Why does \( f(x) \) change its expression for different values of \( x \)?
5. How can you graph a piecewise function?

**Tip:** Always double-check which part of a piecewise function applies before calculating the value.

Find f(8) for this piecewise-defined function. f(x)= 4x–5 if x≤1 1/6(x–1) if x>1. Write your answer as an integer or as a fraction in simplest form. f(8)=

Learn how to evaluate the piecewise-defined function f(x) = 4x - 5 if x ≤ 1 and f(x) = (1/6)(x - 1) if x > 1 by calculating f(8). This problem introduces key concepts in algebra and piecewise functions. Suitable for students in Grades 9-10.

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