Question

find f(6) for this piecewise-defined function.
\\( f(x) = \

$$\begin{cases} 2x - \\frac{1}{4} & \\text{if } x \\leq 5 \\\\ \\frac{1}{3} & \\text{if } x > 5 \\end{cases}$$

\\)
write your answer as an integer or as a fraction in simplest form.
\\( f(6) = \boxed{} \\)

Explanation:

Step1: Determine the relevant piece

Since \( 6 > 5 \), we use the piece of the function defined for \( x > 5 \), which is \( f(x)=\frac{1}{3} \).

Step2: Evaluate \( f(6) \)

Substitute \( x = 6 \) into the relevant piece. Since the piece for \( x > 5 \) is a constant function \( \frac{1}{3} \), \( f(6)=\frac{1}{3} \).

Answer:

\(\frac{1}{3}\)