MHT CET · Maths · Functions
If \([x]\) is greatest integer function and \(2[2 x-5]-1=7\), then \(x\) lies in
- A \(\left[\frac{9}{2}, 5\right)\)
- B \(\left[\frac{9}{2}, 5\right]\)
- C \(\left(\frac{9}{2}, 5\right)\)
- D \(\left(\frac{9}{2}, 5\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\frac{9}{2}, 5\right)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 2[2 x-5]-1=7 \\ & \Rightarrow 2[2 x]-10-1=7 \\ & \Rightarrow[2 x]=9 \\ & \Rightarrow 9 \leq 2 x<10 \\ & x \in\left[\frac{9}{2}, 5\right)\end{aligned}\)
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