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CUET · MATHS · PYQ PAPER 2023

If \(f(x)=\frac{1}{2 x+1}, x \neq-\frac{1}{2}\), then \(f[f(x)]\) is :

  1. A \(\frac{2 x+1}{2 x+3}\), provided \(x \neq-\frac{1}{2}\) and \(x \neq-\frac{3}{2}\)
  2. B \(\frac{2 x+1}{2 x+3}\)
  3. C \(\frac{3 x+3}{2 x+1}\)
  4. D \(\frac{2 x+3}{2 x+1}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{2 x+1}{2 x+3}\), provided \(x \neq-\frac{1}{2}\) and \(x \neq-\frac{3}{2}\)

Step-by-step Solution

Detailed explanation

\(f[f(x)] = \frac{1}{2\left(\frac{1}{2x+1}\right)+1}\) \(f[f(x)] = \frac{1}{\frac{2}{2x+1}+1}\) \(f[f(x)] = \frac{1}{\frac{2+(2x+1)}{2x+1}}\) \(f[f(x)] = \frac{1}{\frac{2x+3}{2x+1}}\) \(f[f(x)] = \frac{2x+1}{2x+3}\), provided \(x \neq-\frac{1}{2}\) and \(x \neq-\frac{3}{2}\)