Question

plz solve this sum...​

Answer 1

take x common in numerator

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Answer 2

$\mathsf{Given :\;y = f(x) = \dfrac{ax - b}{bx - a}}$

In order to find f(y), We need to replace x with y

$\mathsf{\implies f(y) = \dfrac{ay - b}{by - a}}$

$\mathsf{But,\;y = \dfrac{ax - b}{bx - a}}$

Substituting the value of y in f(y), We get :

$\mathsf{\implies f(y) = \dfrac{a\bigg(\dfrac{ax - b}{bx - a}\bigg) - b}{b\bigg(\dfrac{ax - b}{bx - a}\bigg) - a}}$

$\mathsf{\implies f(y) = \dfrac{\dfrac{a(ax - b)}{bx - a} - b}{\dfrac{b(ax - b)}{bx - a} - a}}$

$\mathsf{\implies f(y) = \dfrac{\dfrac{a(ax - b) - b(bx - a)}{bx - a}}{\dfrac{b(ax - b) - a(bx - a)}{bx - a}}}$

$\mathsf{\implies f(y) = \dfrac{a(ax - b) - b(bx - a)}{b(ax - b) - a(bx - a)}}$

$\mathsf{\implies f(y) = \dfrac{a^2x - ab - b^2x + ab}{abx - b^2 - abx + a^2}}$

$\mathsf{\implies f(y) = \dfrac{a^2x - b^2x}{a^2 - b^2}}$

$\mathsf{\implies f(y) = \dfrac{x(a^2 - b^2)}{a^2 - b^2}}$

$\mathsf{\implies f(y) = x}$