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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
MCQ
Choose the correct answer from the given four options. Let
$\text{f}:\text{R}-\Big\{\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be defined by $\text{f}(\text{x})=\frac{3\text{x}+2}{5\text{x}-3}.$ Then,
  • ✓
    $\text{f}^{-1}(\text{x})=\text{f}(\text{x})$
  • B
    $\text{f}^{-1}(\text{x})=-\text{f}(\text{x})$
  • C
    $(\text{fof})\text{x}=-\text{x}$
  • D
    $\text{f}^{-1}\text{x}=\frac{1}{19}\text{f}(\text{x})$
✓

Answer

Correct option: A.
$\text{f}^{-1}(\text{x})=\text{f}(\text{x})$
We have, $\text{f}(\text{x})=\frac{3\text{x}+2}{5\text{x}-3}=\text{y}\ ($let$)$
$\Rightarrow\ 3\text{x}+2=5\text{xy}-3\text{y}$
$\Rightarrow\ \text{x}(3-5\text{y})=-3\text{y}-2$
$\Rightarrow\ \text{x}=\frac{3\text{y}+2}{5\text{y}-3}$
$\Rightarrow\ \text{f}^{-1}(\text{x})=\frac{3\text{x}+2}{5\text{x}-3}$
$\therefore\ \text{ f}^{-1}\text{x}=\text{f}(\text{x})$

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