Question:
In the interval \( (7, \infty) \), the function \( f(x) = |x - 5| + 2|x - 7| \) is:
In the interval \( (7, \infty) \), the function \( f(x) = |x - 5| + 2|x - 7| \) is:
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Break absolute value functions into piecewise expressions to determine monotonicity.
Updated On: May 17, 2025
- Increasing function
- Decreasing function
- Constant function
- Attains maximum value
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The Correct Option is A
Solution and Explanation
In \( x>7 \):
\[
\begin{align}
|x - 5| = x - 5,\quad |x - 7| = x - 7 \Rightarrow f(x) = (x - 5) + 2(x - 7) = x - 5 + 2x - 14 = 3x - 19
\]
Clearly, this is a linear function with positive slope, so it's strictly increasing.
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