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If Y = F ( X ) = a X − B B X − a , Show that X = F(Y). - Mathematics

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Question

If  \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).

 

 

Solution

Given:

\[f\left( x \right) = \frac{ax - b}{bx - a}\]
Let y = f (x) .
⇒ ybx -a) = ax  b 
⇒ xyb – ay = ax – 
⇒ xyb – ax = ay – b
⇒ x(by – a) = ay – 
\[\Rightarrow x = \frac{ay - b}{by - a}\]
⇒ x = f (y)      
Hence proved.
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Chapter 3: Functions - Exercise 3.2 [Page 11]

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RD Sharma Mathematics [English] Class 11
Chapter 3 Functions
Exercise 3.2 | Q 3 | Page 11

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