Question

find f(1) for this piecewise-defined function.
\\( f(x) = \

$$\begin{cases} 2x - 1 & \\text{if } x < -1 \\\\ 6 & \\text{if } -1 \\leq x \\leq 2 \\\\ \\frac{3}{2}x & \\text{if } x > 2 \\end{cases}$$

\\)
write your answer as an integer or as a fraction in simplest form.
f(1) = \boxed{\quad}
submit

Explanation:

Step1: Determine the interval for \( x = 1 \)

Check which piece of the piecewise function applies to \( x = 1 \). The intervals are \( x < -1 \), \( -1 \leq x \leq 2 \), and \( x > 2 \). Since \( -1 \leq 1 \leq 2 \), we use the middle piece.

Step2: Evaluate the function at \( x = 1 \)

The middle piece is \( f(x) = 6 \) for \( -1 \leq x \leq 2 \). So when \( x = 1 \), \( f(1) = 6 \).

Answer:

\( 6 \)