JEE Mains · Maths · STD 12 - 1. relation and function
The function \(f:(-\infty, \infty) \rightarrow(-\infty, 1),\) defined by \(f(x)=\frac{2^x-2^{-x}}{2^x+2^{-x}} \text { is : }\)
- A Neither one-one nor onto
- B Onto but not one-one
- C Both one-one and onto
- D One-one but not onto
Answer & Solution
Correct Answer
(D) One-one but not onto
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{f}(\mathrm{x})=\frac{2^{2 \mathrm{x}}-1}{2^{2 \mathrm{x}}+1} \\ & =1-\frac{2}{2^{2 \mathrm{x}}+1} \\ & \mathrm{f}^{\prime}(\mathrm{x})=\frac{2}{\left(2^{2 \mathrm{x}}+1\right)^2} \cdot 2.2^{2 \mathrm{x}} \cdot \ln 2 \text { i.e always }+\mathrm{ve}…
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