AP EAMCET · Maths · Functions
If \(f: R \rightarrow R\) is defined by \(f(x)=[2 x]-2[x]\) for \(x \in R\), where \([x]\) is the greatest integer not exceeding \(x\), then the range of \(f\) is :
- A \(\{x \in R: 0 \leq x \leq 1\}\)
- B \(\{0,1\}\)
- C \(\{x \in R: x>0\}\)
- D \(\{x \in R: x \leq 0\}\)
Answer & Solution
Correct Answer
(B) \(\{0,1\}\)
Step-by-step Solution
Detailed explanation
\(\because \quad f(x)=[2 x]-2[x] \forall x \in R\) Let \(x\) is an integer, then \(f(x)=0\) and let \(x\) is not an integer, then \(quad f(x)=1\) \(\therefore\) Range of \(f(x)=\{0,1\}\)
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