CUET · MATHS · PYQ PAPER 2023
Let \(f:[0, \infty) \rightarrow[0,2]\) be defined by \(f(x)=\frac{2 x}{1+x}\), then \(f\) is:
- A one one but not onto
- B onto but not one one
- C both one one and onto
- D neither one one nor onto
Answer & Solution
Correct Answer
(A) one one but not onto
Step-by-step Solution
Detailed explanation
Let \(f(x_1) = f(x_2)\). \(\frac{2x_1}{1+x_1} = \frac{2x_2}{1+x_2}\) \(2x_1(1+x_2) = 2x_2(1+x_1)\) \(2x_1+2x_1x_2 = 2x_2+2x_1x_2\) \(x_1 = x_2\). Thus, \(f\) is one one. Let \(y = f(x)\). \(y = \frac{2x}{1+x}\) \(y(1+x) = 2x\) \(y+yx = 2x\) \(y = x(2-y)\) \(x = \frac{y}{2-y}\)…
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