If $y=f(x)=\frac{3x-5}{2x-m}$ find $m$ so that $f(y)=x$. Question: If $y=f(x)=\dfrac{3x-5}{2x-m}$ find $m$ so that $f(y)=x$.
We have $y=\dfrac{3\left(\frac{3x-5}{2x-m}\right)-5}{2\left(\frac{3x-5}{2x-m}\right)-m} $
How can I find $m$? It is given than $m=3$.

Now, $$\dfrac{3\left(\frac{3x-5}{2x-m}\right)-5}{2\left(\frac{3x-5}{2x-m}\right)-m}=x$$ or
$$\frac{3(3x-5)-5(2x-m)}{2(3x-5)-m(2x-m)}=x$$ or
$$\frac{-x+5m-15}{x(6-2m)+m^2-10}=x$$ or $$-x+5m-15=x^2(6-2m)+x(m^2-10).$$
We need $$5m-15=0,$$ $$6-2m=0$$ and $$m^2-10=-1,$$ which gives $m=3.$
