Question

If y=f(x)=ax-b/bx-a prove that f(y)=x

Answer 1

Given f(x) = y =(ax - b)/(cx - a)

=> y*(cx - a) = ax - b

=> cxy-ay = ax - b

=>cxy- ax = ay - b

=> x*(cy - a) = ay - b

=> x =  (ay - b)/(cy - a)

=>f(y) = x = (ay - b)/(cy - a)

Answer 2

Answer:

$f(y)=x={\frac{ay-b}{by-a}$

Step-by-step explanation:

It is given that $y=f(x)={\frac{ax-b}{bx-a}$

Cross-multiplying the above equation, we get

⇒$y(bx-a)=ax-b$

⇒$ybx-ay=ax-b$

⇒$ybx-ax=-b+ay$

⇒$x(yb-a)=ay-b$

⇒$x={\frac{ay-b}{by-a}$

Thus, $f(y)=x={\frac{ay-b}{by-a}$

Hence proved