Questions: Find (f(5))

Find (f(5))
Transcript text: Find $f(5)$
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Solution

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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 \( x = 5 \).

Step 1: Identify the Relevant Interval 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 \( 1 < x < 5 \)
Step 2: Determine if \( x = 5 \) Falls Within Any Interval

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.
Step 3: Conclusion on the Definition of \( f(5) \)

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

Final Answer

The function \( f(x) \) is not defined for \( x = 5 \). Therefore, the value of \( f(5) \) is \(\boxed{\text{undefined}}\).

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