Question 34664
{{{ f(x)= x/(3-x) }}} --> its domain is any real value of x but not x=3. This is because when x=3, the denominator is then zero and any fraction having a zero denominator gives "ERROR" on your calculator, so HAS TO BE avoided.


Inverse:
{{{ y = x/(3-x) }}}
{{{ y(3-x) = x }}}
{{{ 3y-xy = x }}}
{{{ 3y-xy-x = 0 }}}
{{{ -xy-x = -3y }}}
{{{ -x(y+1) = -3y }}}
{{{ x(y+1) = 3y }}}
{{{ x = (3y)/(y+1) }}}


so, here we have {{{ f(y) = (3y)/(y+1) }}}, or seeing as how we usually quote equations in terms of x: {{{ f(x) = (3x)/(x+1) }}}. And as this is the inverse function of the original, then we can say: {{{ f^(-1)(x) = (3x)/(x+1) }}}


Its domain is: any real value of x but not x=-1 for exactly the same reason as before.


jon