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MHT CET · Maths · Functions

If \(f(x)=\frac{x}{2 x+1}\) and \(g(x)=\frac{x}{x+1}\), then \((f \circ g)(x)=\)

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

Answer & Solution

Correct Answer

(B) \(\frac{x}{3 x+1}\)

Step-by-step Solution

Detailed explanation

\(
\begin{aligned}
& (f \circ g)(x)=f\left[\frac{x}{x+1}\right] \\
& =\frac{\left(\frac{x}{x+1}\right)}{2\left(\frac{x}{x+1}\right)+1}=\frac{x}{x+1} \times \frac{x+1}{2 x+x+1}=\frac{x}{3 x+1}
\end{aligned}
\)
\(\begin{aligned} & (f \circ g)(x)=f\left[\frac{x}{x+1}\right] \\ & =\frac{\left(\frac{x}{x+1}\right)}{2\left(\frac{x}{x+1}\right)+1}=\frac{x}{x+1} \times \frac{x+1}{2 x+x+1}=\frac{x}{3 x+1}\end{aligned}\)