Question

Given, if y=f(x)=(2x+1)/(3x-m) and if f(y)=x, Find m.

Answer 1

Given

$y=f(x)=\dfrac{2x+1}{3x-m}$

$f(y)=x$

To find

Value of $m$

Solution

$f(y)=x\\\Rightarrow \dfrac{2y+1}{3y-m} =x$

Taking x to be 0 in the first equation we get

$y=\dfrac{2x+1}{3x-m}\\\Rightarrow y=\dfrac{1}{-m}\\\Rightarrow y=-\dfrac{1}{m}$

So

$x=\dfrac{2\times-\dfrac{1}{m}+1}{3\times -\dfrac{1}{m}-m}$

Taking $x =0$

$0=\dfrac{2\times-\dfrac{1}{m}+1}{3\times -\dfrac{1}{m}-m}\\\Rightarrow 0=2\times-\dfrac{1}{m}+1\\\Rightarrow m=\dfrac{1}{2}$

So, $\mathbf{m=\dfrac{1}{2}}$