WBJEE · Maths · Functions
\(f: X \rightarrow \mathbb{R}, X=\{x \mid 0 < x < 1\}\) is defined as \(f(x)=\frac{2 x-1}{1-|2 x-1|}\). Then
- A \(\mathrm{f}\) is only injective
- B \(f\) is only surjective
- C \(\mathrm{f}\) is bijective
- D f is neither injective nor surjective
Answer & Solution
Correct Answer
(C) \(\mathrm{f}\) is bijective
Step-by-step Solution
Detailed explanation
Put \(2 \mathrm{x}-1=\mathrm{t}\), then the function becomes \(\begin{aligned} &f(t)=\frac{t}{1-|t|},-1 0 \forall-1 < t < 1\) \(\therefore\) f is injective
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