First slide

Algebra of real valued functions

Question

If f(x)= $\frac{a x - c}{c x - a}$ =y,then f(y) equals

Easy

A

x
B

1/x
C

1
D

0

Solution

Given
$y = \frac{a x - c}{c x - a} \Rightarrow c x y - a y = a x - c \Rightarrow c x y - a x = a y - c \Rightarrow x (c y - a) = a y - c ∴ x = \frac{a y - c}{c y - a} = f (y)$

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