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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS2 Marks
Question
Let $\text{f}:\text{R}-\Big\{-\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be a function defined as $\text{f(x)}=\frac{2\text{x}}{5\text{x}+3}.$ Write $f^{-1}$: Range of $\text{f}\rightarrow\ \text{R}-\Big\{-\frac{3}{5}\Big\}.$
✓

Answer

Let $f^{-1}(x) = y$ ......(1) ⇒ f(y) = x$\Rightarrow\ \frac{2\text{y}}{5\text{y}+3}=3\text{x}$
$⇒ 2y = 5xy + 3x ⇒ 2y - 5xy = 3x ⇒ y(2 - 5x) = 3x \Rightarrow\ \text{y}=\frac{3\text{x}}{2-5\text{x}}$ $\Rightarrow\ \text{f}^{-1}(\text{x})=\frac{3\text{x}}{2-5\text{x}}$ [from 1]

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