Question 917830

{{{ f(x)= (x+4)/(x-2) }}}

find {{{f^-1(y)}}}

since {{{f(x)=y}}} we have

{{{ y = (x+4)/(x-2)}}} ...swap {{{x}}} and {{{y}}}

{{{ x = (y+4)/(y-2)}}} .......solve for {{{y}}}

{{{ x(y-2) = y+4 }}} 

{{{ x*y-2x = y+4 }}} 

{{{ -2x-4 = y-xy }}} 

{{{ -2x-4 = y(1-x) }}} 

{{{ (-2x-4)/(1-x) = y }}} 

{{{ y=-2(x+2)/(-(x-1)) }}}

{{{ y=2(x+2)/(x-1) }}}


the range of {{{f(x)}}}:

{ {{{f}}} element {{{R}}} : {{{f<>1}}} }
(assuming a function from reals to reals)