Question

Y=f(x)=5x-3/3x-5, show that f(y) =x

Answer 1

Answer:

Given,

$\sf \: y = f(x) = \frac{5x - 3}{3x - 5} \\ \sf \therefore \: \: \: \: y = \frac{5x - 3}{3x - 5} \\ \sf \implies \: y(3x - 5) = 5x - 3 \\ \sf \implies \: 3xy - 5y = 5x - 3 \\ \sf \implies \: 3xy - 5x = 5y - 3 \\ \sf \implies \: x(3y - 5) = 5y - 3 \\ \sf \implies \: x = \frac{5y - 3}{3y - 5} \: \: \: \: \: - - - - (1) \\ \\ \bf again \: \\ \sf \: \: \: \: \: \: \: \: \: \: \: f(x) = \frac{5x - 3}{3x - 5} \\ \sf \implies \: f(y) = \frac{5y - 3}{3y - 5} \: \: \: \: \: - - - - (2) \\ \\ \sf \: by \: comparing \: eqn.(1) \: \: and \: \: eqn.(2) \\ \sf \: we \: can \: write \: that \:, \\ \\ \sf \: f(y) = \frac{5y - 3}{3y - 5} = x \\ \sf \therefore \: f(y) = x \\ \\ \huge\red{ \underline{\green{ ( \sf \: hence \: showed)}}}$