MHT CET · Maths · Functions
\(\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}\) is defined by \(f(x)=\frac{3 x-2}{5 x+3}\), then \(f \circ f(1)\) is
- A \(1\)
- B \(\frac {-13}{29}\)
- C \(\frac {13}{29}\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(\frac {-13}{29}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=\frac{3 x-2}{5 x+3} \\ & \begin{aligned} f(f(x)) & =\frac{3\left(\frac{3 x-2}{5 x+3}\right)-2}{5\left(\frac{3 x-2}{5 x+3}\right)+3} \\ & =\frac{3(3 x-2)-2(5 x+3)}{5(3 x-2)+3(5 x+3)} \\ & =\frac{9 x-6-10 x-6}{15 x-10+15 x+9} \\ & =\frac{-x-12}{30 x-1}\end{aligned} \\ & \text { fof }(1)=\frac{-1-12}{30-1}=\frac{-13}{29}\end{aligned}\)
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