Question 375581
{{{f(x)=2x+1}}} Start with the given function.



{{{f(g(x))=2(g(x))+1}}} Plug in {{{x=g(x)}}}



{{{f(g(x))=2((x-1)/2)+1}}} Plug in {{{g(x)=(x-1)/2}}} on the right side.



{{{f(g(x))=cross(2)((x-1)/cross(2))+1}}} Cancel the common terms.



{{{f(g(x))=x-1+1}}} Simplify.



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




Note: if you show that g(f(x))=x as well, then you've shown the f and g are inverse functions of each other.



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