JEE Mathematics 2023 Question with Solution

Given:

$$f(x) = \frac{x^2 + 2x + 1}{x + 1}$$

Find: Whether $f(x)$ is one-one or many-one on the stated intervals.

The solution rewrites and analyzes a different function:

$$f(x) = \frac{x^2 + 2x + 1}{x^2 + 1}$$

and concludes that the correct option is B. Since the solution conclusion is the primary source, the extracted answer is B.

Also, from the given question expression itself,

$$x^2 + 2x + 1 = (x+1)^2$$

so for $x \neq -1$,

$$f(x) = \frac{(x+1)^2}{x+1} = x+1$$

This shows the given question text and the provided the solution are inconsistent with each other. The answer has therefore been taken from the solution as instructed, despite this discrepancy.

Given: The question states

$$f(x) = \frac{x^2 + 2x + 1}{x + 1}$$

while the solution works with

$$f(x) = \frac{x^2 + 2x + 1}{x^2 + 1} = 1 + \frac{2x}{x^2 + 1}$$

Find: Which source determines the answer.

The solution explicitly says The Correct Option is B and its working is based on the denominator $x^2+1$, not $x+1$. Therefore, these provided inputs refer to mismatched statements. Under the, the solution is treated as authoritative for the answer, so the recorded answer is B.

The source mismatch should be reviewed manually.