AP EAMCET · Maths · Functions
\([\mathrm{t}]\) denotes the greatest integer function and \([\mathrm{t}-\mathrm{m}]=[\mathrm{t}]-\mathrm{m}\) when \(\mathrm{m} \in \mathrm{Z}\). If \(\mathrm{k}=2[2 \mathrm{x}-1]-1\) and \(3[2 \mathrm{x}-2]+1=2[2 \mathrm{x}-1]-1\) then the range of \(\mathrm{f}(\mathrm{x})=\) \([\mathrm{k}+5 \mathrm{x}]\) is
- A \(\{7,8,9\}\)
- B \(\{4,5,6\}\)
- C \(\{5,6,7\}\)
- D \(\{6,7,8\}\)
Answer & Solution
Correct Answer
(D) \(\{6,7,8\}\)
Step-by-step Solution
Detailed explanation
\(3([2x-1]-1)+1 = 2[2x-1]-1\) \(3[2x-1]-2 = 2[2x-1]-1\) \([2x-1] = 1\) \(k = 2[2x-1]-1 = 2(1)-1 = 1\) \(1 \le 2x-1 \(2 \le 2x \(1 \le x \(5 \le 5x \(6 \le 1+5x \(f(x) = [k+5x] = [1+5x]\) Range of \(f(x) = \{6, 7, 8\}\)
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