AP EAMCET · Maths · Functions
The function \(f: \mathbf{R} \rightarrow \mathbf{R}\) defined by \(f(x)=\frac{x}{\sqrt{1+x^2}}\) is ........
- A Surjective but not injective
- B Bijective
- C Injective but not surjective
- D Neither injective nor surjective
Answer & Solution
Correct Answer
(C) Injective but not surjective
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=\frac{x}{\sqrt{1+x^2}} \\ & f\left(x_1\right)=f(x)_2 \Rightarrow \frac{x_1}{\sqrt{1+x_1^2}}=\frac{x_2}{\sqrt{1+x_2^2}} \end{aligned}\)…
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