JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f: R-\left\{\frac{\alpha}{6}\right\} \rightarrow R\) be defined by \(f(x)=\frac{5 x+3}{6 x-\alpha} .\) Then the value of \(\alpha\) for which \((fof)(x)=x\), for all \(x \in R-\left\{\frac{\alpha}{6}\right\}\), is:
- A \(4\)
- B \(5\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{5 x+3}{6 x-\alpha}=y\,....(i)\) \(5 x+3=6 x y-\alpha y\) \(x(6 y-5)=\alpha y+3\) \(x=\frac{\alpha y+3}{6 y-5}\) \(f^{-1}(x)=\frac{\alpha x+3}{6 x-5}\,....(ii)\) fo \(f(x)=x\) \(f(x)=f^{-1}(x)\) From eq \(^{n}\) \((i)\, \& \,(ii)\) Clearly \(\alpha=5\)
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