Question

If $y=f\left(x\right)=\frac{ax-b}{bx-a},x\ne \frac{a}{b},|a|\ne |b|,$ then $f\left(y\right)=$

• A. $x$
• B. $-x$
• C. $\frac{1}{x}$
• D. $-\frac{1}{x}$

Answer 1

The correct option is A $x$

Given that $y=f\left(x\right)=\frac{ax-b}{bx-a},x\ne \frac{a}{b},|a|\ne |b|.$
$\Rightarrow y(bx-a)=ax-b$
$\Rightarrow byx-ay=ax-b$
$\Rightarrow byx-ax=ay-b$
$\Rightarrow x(by-a)=ay-b$
$\Rightarrow x=\frac{ay-b}{by-a}=f\left(y\right)$