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if y = f(X) = (ax-b)/(bx-a) show that x ...

if y = f(X) = `(ax-b)/(bx-a)` show that x = f(y)

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We have, `y=f(x)=(ax-b)/(bx-a)`.
`:.f(y)=f{f(x)}=f((ax-b)/(ax-))={{a((ax-b)/(bx-a))-b}}/{{b((ax-b)/(bx-a))-a}}`
`={{(a^(2)x-ab)-(b^(2)x-ab)}}/((bx-a))xx((bx-a))/{{(abx-b^(2))-(abx-a^(2))}}`
`=((a^(2)x-b^(2)x))/((a^(2)-b^(2)))=((a^(2)-b^(2))x)/((a^(2)-b^(2)))=x`. Hence, x=f(y).
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