TS EAMCET · Maths · Functions
Which one of the following functions is a bijection?
- A \(f: \mathbb{R}-\mathbb{Z} \rightarrow[0,1]\) defined by \(\mathrm{f}(\mathrm{x})=\sqrt{x-[x]}\). (Here \([x]\) represents the greatest integer function)
- B \(f: \mathbb{R} \rightarrow(-\infty, 2)\) defined by \(\mathrm{f}(\mathrm{x})=4 x-x^2-3\)
- C \(f:(5, \infty) \rightarrow \mathbb{R}-\{0\}\) defined by \(f(x)=\frac{1}{\sqrt{x-5}}\)
- D \(f:[0,4] \rightarrow[0,4]\) defined by \(f(x)=\sqrt{16-x^2}\)
Answer & Solution
Correct Answer
(D) \(f:[0,4] \rightarrow[0,4]\) defined by \(f(x)=\sqrt{16-x^2}\)
Step-by-step Solution
Detailed explanation
(a) \(f(x)=\sqrt{x-[x]}=\sqrt{\{x\}}\) \(\because\{1,2\}=\{2,2\}\) \(\therefore f(x)\) is many one. (b) \(f(x)=4 x-x^2-3\) Clearly it is a quadratic expression with real roots hence many one function. (c) \(f(x)=\frac{1}{\sqrt{x-5}}\) Clearly Range have only positive real…
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