If f(x) = frac{3x+2}{5x-3},where x in R - {fr | vedclass

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(A) Let $y = f(x) = \frac{3x+2}{5x-3}$.Then $y(5x - 3) = 3x + 2$.Expanding this,we get $5xy - 3y = 3x + 2$.Rearranging the terms to solve for $x$,we h

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$f^{-1}(x) = f(x)$

Vedclass · Answer

(A) Let $y = f(x) = \frac{3x+2}{5x-3}$.Then $y(5x - 3) = 3x + 2$.Expanding this,we get $5xy - 3y = 3x + 2$.Rearranging the terms to solve for $x$,we have $5xy - 3x = 3y + 2$.Factoring out $x$,we get $x(5y - 3) = 3y + 2$.Thus,$x = \frac{3y+2}{5y-3}$.By definition,$f^{-1}(y) = x = \frac{3y+2}{5y-3}$.Replacing $y$ with $x$,we obtain $f^{-1}(x) = \frac{3x+2}{5x-3}$.Since $f^{-1}(x) = f(x)$,the correct option is $A$.

If $f(x) = \frac{3x+2}{5x-3}$,where $x \in R - \{\frac{3}{5}\}$,then:

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