JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f: R -\{3\} \rightarrow R -\{1\}\) be defined by \(f(x)=\frac{x-2}{x-3} .\) Let \(g: R \rightarrow R\) be given as \(g ( x )=2 x -3\). Then, the sum of all the values of \(x\) for which \(f^{-1}( x )+ g ^{-1}( x )=\frac{13}{2}\) is equal to ...... .
- A \(7\)
- B \(2\)
- C \(5\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(f(x)=y=\frac{x-2}{x-3}\) \(\therefore x=\frac{3 y-2}{y-1}\) \(\therefore f^{-1}(x)=\frac{3 x-2}{x-1}\) \( g(x)=y=2 x-3\) \(\therefore x=\frac{y+3}{2}\) \(\therefore g^{-1}(x)=\frac{x+3}{2}\) \(\because f^{-1}(x)+g^{-1}(x)=\frac{13}{2}\) \(\therefore x^{2}-5 x+6=0\)…
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