Question 1095376
<br>I will assume that by "(f.g)^-1(x)" you mean the inverse of the composition of functions f and g; that is,
{{{((f(g(x)))^-1)}}}<br>
In that case, the problem is asking you to find the input value x for which
{{{f(g(x)) = 5/3}}}<br>
Then
{{{f(g(x)) = (3x+5)/((3x+5)-3) = (3x+5)/(3x+2)}}}
so
{{{(3x+5)/(3x+2) = 5/3}}}
{{{9x+15 = 15x+10}}}
{{{5 = 6x}}}
{{{x = 5/6}}}<br>
Check:
{{{g(5/6) = 3(5/6)+5 = 5/2+5 = 15/2}}}
{{{f(15/2) = (15/2)/((15/2)-3) = (15/2)/(9/2) = 15/9 = 5/3}}}