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प्रश्न
If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.
उत्तर
We have, f(x) = y = `(ax - b)/(cx - a)`
∴ f(y) = `(ay - b)/(cy - a)`
= `(a((ax - b)/(cx - a)) - b)/(c((ax - b)/(cx - a)) - a)`
= `(a(ax - b) - b(cx - a))/(c(ax - b) - a(cx - a))`
= `(a^2x - ab - bcx + ab)/(acx - bc - acx + a^2)`
= `(a^2x - bcx)/(a^2 - bc)`
= `(x(a^2 - bc))/((a^2 - bc))`
∴ f(y) = x
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