Q71 / 150 · MHT CET 2023 (09 May Shift 1) · Mathematics

$\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}$ is defined by $f(x)=\frac{3 x-2}{5 x+3}$, then $f \circ f(1)$ is

  • A
    $1$
  • Correct answer
    B
    $\frac {-13}{29}$
  • C
    $\frac {13}{29}$
  • D
    $-1$

Solution

$\begin{aligned} & f(x)=\frac{3 x-2}{5 x+3} \\ & \begin{aligned} f(f(x)) & =\frac{3\left(\frac{3 x-2}{5 x+3}\right)-2}{5\left(\frac{3 x-2}{5 x+3}\right)+3} \\ & =\frac{3(3 x-2)-2(5 x+3)}{5(3 x-2)+3(5 x+3)} \\ & =\frac{9 x-6-10 x-6}{15 x-10+15 x+9} \\ & =\frac{-x-12}{30 x-1}\end{aligned} \\ & \text { fof }(1)=\frac{-1-12}{30-1}=\frac{-13}{29}\end{aligned}$

Hence, the correct answer is option: 'B'.

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