Question 1061291
Use x,y nomenclature.
{{{y=(8x-3)/(3x+5)}}}
Interchange x and y,
{{{x=(8y-3)/(3y+5)}}}
{{{(3y+5)x=8y-3}}}
{{{3xy+5x=8y-3}}}
{{{3xy-8y=-3-5x}}}
{{{(3x-8)y=-3-5x}}}
{{{y=(3+5x)/(8-3x)}}}
{{{h^(-1)(x)=(3+5x)/(8-3x)}}}
Domain is all x except,
{{{8-3x=0}}}
{{{8=3x}}}
{{{x=8/3}}}
Determine the range from the domain of the original function,
{{{3x+5=0}}}
{{{3x=-5}}}
{{{x=-5/3}}}
Since {{{x=-5/3}}} is excluded from h domain, it is also excluded from the inverse's range.