Questions: Find (f(5))

Solution Steps

To find \( f(5) \), we need to determine which piece of the piecewise function applies when \( x = 5 \). The function is defined for three intervals: \( x < 1 \), \( x = 1 \), and \( 1 < x < 5 \). Since \( x = 5 \) does not fall into any of these intervals, the function is not defined for \( x = 5 \).

The function \( f(x) \) is defined as a piecewise function with the following intervals:

• \( f(x) = 5x - 9 \) for \( x < 1 \)
• \( f(x) = 2 \) for \( x = 1 \)
• \( f(x) = -x - 3 \) for \( 1 < x < 5 \)

We need to check if \( x = 5 \) falls within any of the defined intervals:

• \( x < 1 \): \( 5 \) does not satisfy this condition.
• \( x = 1 \): \( 5 \) does not satisfy this condition.
• \( 1 < x < 5 \): \( 5 \) does not satisfy this condition.

Since \( x = 5 \) does not fall within any of the specified intervals, the function \( f(x) \) is not defined for \( x = 5 \).

Final Answer