Question 153022
{{{f(x)=3x-4}}} Start with the first function.



{{{f(g(x))=3((x+4)/3)-4}}} Plug in {{{g(x)=(x+4)/3}}}.



{{{f(g(x))=x+4-4}}} Multiply 



{{{f(g(x))=x}}} Combine like terms



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{{{g(x)=(x+4)/3}}} Start with the second function.



{{{g(f(x))=(3x-4+4)/3}}} Plug in {{{f(x)=3x-4}}} 



{{{g(f(x))=(3x)/3}}} Combine like terms.



{{{g(f(x))=x}}} Reduce.



Since {{{f(g(x))=x}}} and {{{g(f(x))=x}}}, this shows that the two functions are inverses of one another.