TS EAMCET · Maths · Functions
If \(f(x)=\frac{2 x-3}{3 x-2}\) and \(f_n(x)=(f o\) fo \(f o \ldots \ldots . . n\) times \()(x)\), then \(f_{32}(x)=\)
- A \(\frac{2 x-3}{3 x-2}\)
- B \(x\)
- C \(\frac{3 x+2}{2 x+3}\)
- D \(f_{23}(x)\)
Answer & Solution
Correct Answer
(B) \(x\)
Step-by-step Solution
Detailed explanation
If \(f(x)=\frac{a x-b}{b x-a} \Rightarrow f o f(x)=x\) \(\begin{aligned} & f_1(x)=\frac{2 x-3}{3 x-2}=f_3(x)=f_5(x) \\ & f_2(x)=f_4(x)=f_6(x)=\ldots=f_{32}(x)=x\end{aligned}\)
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