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

If $f(x)=\frac{x}{2 x+1}$ and $g(x)=\frac{x}{x+1}$, then $(f \circ g)(x)=$
  1. $\frac{2 x-1}{x+1}$
  2. $\frac{x}{3 x+1}$
  3. $\frac{x+1}{x+2}$
  4. $\frac{x-1}{2 x+1}$

Solution

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

Asked in: MHT CET 2021 (23 Sep Shift 1)

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