Question 312514
{{{f(g)=5((x+5)/6)-6=(1/6)(5x+25-36)=(1/6)(5x-11)}}} which does not equal {{{x}}}
{{{g(f)=(1/6)(5x-6+5)=(1/6)(5x-1)}}} which also does not equal {{{x}}}
No, they are not inverse functions.
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Find the inverse by interchanging x and y in the original f(x) and solving for y.
{{{f(x)=y=5x-6}}}
{{{x=5y-6}}}
{{{x+6=5y}}}
{{{highlight(g(x)=y=(1/5)(x+6))}}}
Now,
{{{f(g)=5((1/5)(x+6))-6=x+6-6=x}}}