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Relations and Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSRelations and Functions3 Marks
Question
If $\text{f(x)}=\text{y}=\frac{\text{ax}-\text{b}}{\text{cx}-\text{a}}$ then prove that f(y) = x.
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Answer

We have, $\text{f(x)}=\text{y}=\frac{\text{ax}-\text{b}}{\text{cx}-\text{a}}$
$\therefore\text{f(y)}=\frac{\text{ay}-\text{b}}{\text{cy}-\text{a}}=\frac{\text{a}\Big(\frac{\text{ax}-\text{b}}{\text{cx}-\text{a}}\Big)-\text{b}}{\text{c}\Big(\frac{\text{ax}-\text{b}}{\text{cx}-\text{a}}\Big)-\text{a}}$
$=\frac{\text{a}(\text{ax}-\text{b})-\text{b}(\text{cx}-\text{a})}{\text{c}(\text{ax}-\text{b})-\text{a}(\text{cx}-\text{a})}$
$=\frac{\text{a}^2\text{x}-\text{ab}-\text{b}\text{cx}+\text{ab}}{\text{a}\text{cx}-\text{bc}-\text{a}\text{cx}+\text{a}^2}$
$=\frac{\text{a}^2\text{x}-\text{b}\text{cx}}{\text{a}^2-\text{bc}}$
$=\frac{\text{x}(\text{a}^2-\text{b}\text{c})}{(\text{a}^2-\text{bc})}$
$\therefore\text{f(y)}=\text{x}$

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