Question 832815
Not sure how you mean your g(x).  As written you have x+3/7, as rendered, {{{x+3/7}}}.


{{{f(g(x))=3(g(x))+7=3(x+3/7)-7}}}
{{{3x+9/7-7}}}
{{{(3x*7)/7+9/7-7*7}}}
{{{(21x+9-7)/7}}}
{{{(21x+2)/7}}}
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Will that composition give x as the result?
NO.


You likely misunderstood what you read of g(x).
This definition is different:  {{{g(x)=(x+3)/7}}}.  Is this what you are really given?

{{{f(g(x))=3((x+3)/7)-7}}}
{{{3(x+3)/7-7*7/7}}}
{{{(3x+9)/7-49/7}}}
{{{(3x+9-49)/7}}}
{{{(3x-40)/7}}}
Neither is this one x.
NOT the inverse of f(x).


The basic idea is if f(g(x))=x and g(f(x))=x, then f and g are inverses.


If you WANT to know the inverse of f(x), then try:
{{{f(g(x))=highlight_green(x=3(g(x))-7)}}} and solve this for g(x).
{{{x+7=3*g(x))}}}
{{{(x+7)/3=(1/3)(3)g(x)}}}
{{{(x+7)/3=g(x)}}}----------This is likely to be the inverse of f(x).