TS EAMCET · Maths · Functions
The range of the real valued function \(f(x)=|x-2|+|x-3|\) is
- A \([3, \infty)\)
- B \([1, \infty)\)
- C \([2, \infty)\)
- D \((0,2] \cup[3, \infty)\)
Answer & Solution
Correct Answer
(B) \([1, \infty)\)
Step-by-step Solution
Detailed explanation
Given function \(\mathrm{f}(\mathrm{x})=|\mathrm{x}-2|+|\mathrm{x}-3|\) We will thick on three point \(\mathrm{x} \leq 2,2 < \mathrm{x} < 3\) and \(\mathrm{x} \geq 3\) For \(\mathrm{x} \leq 2\) \[ f(x)=-x+2-x+3=-2 x+5 \] For \(2 < \mathrm{x} < 3\) \[ f(x)=x-2-x+3=1 \] For,…
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